# Les 20 dernières publications du LPTMS

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## Archive ouverte HAL – Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle

### Francesco Mori

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{1}Pierre Le Doussal^{3}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Pierre Le Doussal, Satya Majumdar, et al.. Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle.

*Physical Review Letters*, American Physical Society, 2020, 124 (9), ⟨10.1103/PhysRevLett.124.090603⟩. ⟨hal-02512214⟩We consider an active run-and-tumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$-component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant rate, we show that $S(t)$ is independent of $d$ for any finite time $t$ (and not just for large $t$), as a consequence of the celebrated Sparre Andersen theorem for discrete-time random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed $v$ of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Universal Scaling of the Velocity Field in Crack Front Propagation

### Clément Le Priol

^{1, 2}Pierre Le Doussal^{1, 2}Laurent Ponson^{3}Alberto Rosso^{4}Julien Chopin^{5}#### Clément Le Priol, Pierre Le Doussal, Laurent Ponson, Alberto Rosso, Julien Chopin. Universal Scaling of the Velocity Field in Crack Front Propagation.

*Physical Review Letters*, American Physical Society, 2020, 124 (6), ⟨10.1103/PhysRevLett.124.065501⟩. ⟨hal-02512228⟩The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.

- 1. FRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. DALEMBERT - Institut Jean Le Rond d'Alembert
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. IF-UFB - Instituto de Fisica, Universidade Federal da Bahia

## Archive ouverte HAL – Universal gap statistics for random walks for a class of jump densities

### Matteo Battilana

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}#### Matteo Battilana, Satya N. Majumdar, Gregory Schehr. Universal gap statistics for random walks for a class of jump densities.

*Markov Processes And Related Fields*, Polymat Publishing Company, 2020. ⟨hal-02518812⟩We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim |\eta|^p \,e^{-|\eta|}$, parametrized by a non-negative integer $p$. Our main focus is on the statistics of the gaps $d_{k,n}$ between two successive maxima $d_{k,n}=M_{k,n}-M_{k+1,n}$ where $M_{k,n}$ is the $k$-th maximum of the RW between step 1 and step $n$. In the limit of large $n$, we show that the probability density function of the gaps $P_{k,n}(\Delta) = \Pr(d_{k,n} = \Delta)$ reaches a stationary density $P_{k,n}(\Delta) \to p_k(\Delta)$. For large $k$, we demonstrate that the typical fluctuations of the gap, for $d_{k,n}= O(1/\sqrt{k})$ (and $n \to \infty$), are described by a non-trivial scaling function that is independent of $k$ and of the jump probability density function $f_p(\eta)$, thus corroborating our conjecture about the universality of the regime of typical fluctuations (see G. Schehr, S. N. Majumdar, Phys. Rev. Lett. 108, 040601 (2012)). We also investigate the large fluctuations of the gap, for $d_{k,n} = O(1)$ (and $n \to \infty$), and show that these two regimes of typical and large fluctuations of the gaps match smoothly.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Two anyons on the sphere: nonlinear states and spectrum

### Alexios P. PolychronakosStéphane Ouvry

^{1}#### Alexios P. Polychronakos, Stéphane Ouvry. Two anyons on the sphere: nonlinear states and spectrum.

*Nucl.Phys.B*, 2020, 951, pp.114906. ⟨10.1016/j.nuclphysb.2019.114906⟩. ⟨hal-02340259⟩We study the energy spectrum of two anyons on the sphere in a constant magnetic field. Making use of rotational invariance we reduce the energy eigenvalue equation to a system of linear differential equations for functions of a single variable, a reduction analogous to separating center of mass and relative coordinates on the plane. We solve these equations by a generalization of the Frobenius method and derive numerical results for the energies of non-analytically derivable states.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order

### Ananyo Maitra

^{1, 2}Pragya SrivastavaM. Cristina MarchettiSriram RamaswamyMartin Lenz^{2, 3}#### Ananyo Maitra, Pragya Srivastava, M. Cristina Marchetti, Sriram Ramaswamy, Martin Lenz. Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order.

*Phys.Rev.Lett.*, 2020, 124 (2), pp.028002. ⟨10.1103/PhysRevLett.124.028002⟩. ⟨hal-02475283⟩We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations, not parallel to the ordering direction, at zero wave number. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature 503, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability.

- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. ESPCI ParisTech

## Archive ouverte HAL – Statistics of first-passage Brownian functionals

### Satya N. Majumdar

^{1}Baruch Meerson#### Satya N. Majumdar, Baruch Meerson. Statistics of first-passage Brownian functionals.

*J.Stat.Mech.*, 2020, 2002 (2), pp.023202. ⟨10.1088/1742-5468/ab6844⟩. ⟨hal-02497830⟩We study the distribution of first-passage functionals of the type where represents a Brownian motion (with or without drift) with diffusion constant D, starting at x 0 > 0, and t f is the first-passage time to the origin. In the driftless case, we compute exactly, for all n > −2, the probability density . We show that has an essential singular tail as and a power-law tail as . The leading essential singular behavior for small A can be obtained using the optimal fluctuation method (OFM), which also predicts the optimal paths of the conditioned process in this limit. For the case with a drift toward the origin, where no exact solution is known for general n > −1, we show that the OFM successfully predicts the tails of the distribution. For it predicts the same essential singular tail as in the driftless case. For it predicts a stretched exponential tail for all n > 0. In the limit of large Péclet number , where is the drift velocity toward the origin, the OFM predicts an exact large-deviation scaling behavior, valid for all A: , where is the mean value of in this limit. We compute the rate function analytically for all n > −1. We show that, while for n > 0 the rate function is analytic for all z, it has a non-analytic behavior at z = 1 for −1 < n < 0 which can be interpreted as a dynamical phase transition. The order of this transition is 2 for −1/2 < n < 0, while for −1 < n < −1/2 the order of transition is ; it changes continuously with n. We also provide an illuminating alternative derivation of the OFM result by using a WKB-type asymptotic perturbation theory for large . Finally, we employ the OFM to study the case of (drift away from the origin). We show that, when the process is conditioned on reaching the origin, the distribution of coincides with the distribution of for with the same .

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Scalable quantum computing with qudits on a graph

### E. O. Kiktenko

^{1}A. S. NikolaevaPeng XuG. V. Shlyapnikov^{2}A. K. Fedorov^{3}#### E. O. Kiktenko, A. S. Nikolaeva, Peng Xu, G. V. Shlyapnikov, A. K. Fedorov. Scalable quantum computing with qudits on a graph.

*Physical Review A*, American Physical Society 2020, 101 (2), ⟨10.1103/PhysRevA.101.022304⟩. ⟨hal-02512218⟩We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multi-qudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for single-qubit operations.

- 1. IPE - Schmidt United Institute of Physics of the Earth [Moscow]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Russian Quantum Center

## Archive ouverte HAL – Reversal of contractility as a signature of self-organization in cytoskeletal bundles

### Martin Lenz

^{1}#### Martin Lenz. Reversal of contractility as a signature of self-organization in cytoskeletal bundles.

*eLife*, eLife Sciences Publication, 2020, 9, ⟨10.7554/eLife.51751⟩. ⟨hal-02518848⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Optimizing Brownian escape rates by potential shaping

### Marie Chupeau

^{1}Jannes GladrowAlexei Chepelianskii^{2}Ulrich F. KeyserEmmanuel Trizac^{1}Ulrich Keyser#### Marie Chupeau, Jannes Gladrow, Alexei Chepelianskii, Ulrich F. Keyser, Emmanuel Trizac, et al.. Optimizing Brownian escape rates by potential shaping.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2020, 117 (3), pp.1383-1388. ⟨10.1073/pnas.1910677116⟩. ⟨hal-02512216⟩Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under two different regularizations, and uncover the efficiency of N-shaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the low-friction inertial regime.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPCT - Laboratoire de Physico-Chimie Théorique

## Archive ouverte HAL – Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids

### Alessandro Manacorda

^{1}Gregory Schehr^{2}Francesco Zamponi^{3}#### Alessandro Manacorda, Gregory Schehr, Francesco Zamponi. Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids.

*Journal of Chemical Physics*, American Institute of Physics, 2020, 152 (16), pp.164506. ⟨10.1063/5.0007036⟩. ⟨hal-02554137⟩- 1. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris

## Archive ouverte HAL – Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes

### Guillaume Lamour

^{1}Antoine Allard^{2}Juan Pelta^{3}Sid Labdi^{3}Martin Lenz^{4}Clément Campillo^{3}#### Guillaume Lamour, Antoine Allard, Juan Pelta, Sid Labdi, Martin Lenz, et al.. Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes.

*Physical Review X*, American Physical Society, 2020, 10 (1), ⟨10.1103/PhysRevX.10.011031⟩. ⟨hal-02512272⟩- 1. LNPC - Neuro-Physique Cellulaire
- 2. Université Laval
- 3. LAMBE - UMR 8587 - Laboratoire Analyse et Modélisation pour la Biologie et l'Environnement
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Locally quasi-stationary states in noninteracting spin chains

### Maurizio Fagotti

^{1}#### Maurizio Fagotti. Locally quasi-stationary states in noninteracting spin chains.

*SciPost Phys.*, 2020, 8, pp.048. ⟨10.21468/SciPostPhys.8.3.048⟩. ⟨hal-02423699⟩Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections").

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Finite-time adiabatic processes: Derivation and speed limit

### Carlos Plata

^{1}David Guéry-Odelin^{2}Emmanuel Trizac^{3}Antonio Prados^{4}#### Carlos Plata, David Guéry-Odelin, Emmanuel Trizac, Antonio Prados. Finite-time adiabatic processes: Derivation and speed limit.

*Physical Review E*, American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032129⟩. ⟨hal-02535447⟩Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant both at the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression/decompression situation.

- 1. Padova University
- 2. Atomes Froids (LCAR)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Universidad de Sevilla

## Archive ouverte HAL – Few-body bound states of two-dimensional bosons

### G. Guijarro

^{1}G. E. Astrakharchik^{1}J. Boronat^{1}B. BazakD. S. Petrov^{2}#### G. Guijarro, G. E. Astrakharchik, J. Boronat, B. Bazak, D. S. Petrov. Few-body bound states of two-dimensional bosons.

*Physical Review A*, American Physical Society 2020, ⟨10.1103/PhysRevA.101.041602⟩. ⟨hal-02537195⟩We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a two-dimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atom-dimer interaction switches to repulsion.

- 1. UPC - Universitat Politècnica de Catalunya [Barcelona]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Extreme value statistics of correlated random variables: a pedagogical review

### Satya N. Majumdar

^{1}Arnab PalGregory Schehr^{1}#### Satya N. Majumdar, Arnab Pal, Gregory Schehr. Extreme value statistics of correlated random variables: a pedagogical review.

*Physics Reports*, Elsevier, 2020, ⟨10.10667⟩. ⟨hal-02512248⟩Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way to physics of disordered systems where one is interested in the statistics of the ground state energy. While the EVS of `uncorrelated' variables are well understood, little is known for strongly correlated random variables. Only recently this subject has gained much importance both in statistical physics and in probability theory. In this review, we will first recall the classical EVS for uncorrelated variables and discuss the three universality classes of extreme value limiting distribution, known as the Gumbel, Fr\'echet and Weibull distribution. We then show that, for weakly correlated random variables with a finite correlation length/time, the limiting extreme value distribution can still be inferred from that of the uncorrelated variables using a renormalisation group-like argument. Finally, we consider the most interesting examples of strongly correlated variables for which there are very few exact results for the EVS. We discuss few examples of such strongly correlated systems (such as the Brownian motion and the eigenvalues of a random matrix) where some analytical progress can be made. We also discuss other observables related to extremes, such as the density of near-extreme events, time at which an extreme value occurs, order and record statistics, etc.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

### Urna Basu

^{1}Satya N. Majumdar^{2}Alberto Rosso^{2}Sanjib Sabhapandit^{3}Gregory Schehr^{2}#### Urna Basu, Satya N. Majumdar, Alberto Rosso, Sanjib Sabhapandit, Gregory Schehr. Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap.

*Journal of Physics A: Mathematical and General*, IOP Publishing, 2020, ⟨10.10083⟩. ⟨hal-02512239⟩We study the motion of a one-dimensional run-and-tumble particle with three discrete internal states in the presence of a harmonic trap of stiffness $\mu.$ The three internal states, corresponding to positive, negative and zero velocities respectively, evolve following a jump process with rate $\gamma$. We compute the stationary position distribution exactly for arbitrary values of $\mu$ and $\gamma$ which turns out to have a finite support on the real line. We show that the distribution undergoes a shape-transition as $\beta=\gamma/\mu$ is changed. For $\beta<1,$ the distribution has a double-concave shape and shows algebraic divergences with an exponent $(\beta-1)$ both at the origin and at the boundaries. For $\beta>1,$ the position distribution becomes convex, vanishing at the boundaries and with a single, finite, peak at the origin. We also show that for the special case $\beta=1,$ the distribution shows a logarithmic divergence near the origin while saturating to a constant value at the boundaries.

- 1. Theoretical Condensed Matter Physics Division
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Raman Research Institute

## Archive ouverte HAL – Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate

### M. Isoard

^{1}N. Pavloff^{1}#### M. Isoard, N. Pavloff. Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate.

*Phys.Rev.Lett.*, 2020, 124 (6), pp.060401. ⟨10.1103/PhysRevLett.124.060401⟩. ⟨hal-02317273⟩We study the quantum fluctuations in a one-dimensional Bose-Einstein condensate realizing an analogous acoustic black hole. The taking into account of evanescent channels and of zero modes makes it possible to accurately reproduce recent experimental measurements of the density correlation function. We discuss the determination of Hawking temperature and show that in our model the analogous radiation presents some significant departure from thermality.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Asymptotic behavior of the length of the longest increasing subsequences of random walks

### J. Ricardo G. Mendonça

^{1}Hendrik Schawe^{2}Alexander K. Hartmann^{3}Alexander Hartmann#### J. Ricardo G. Mendonça, Hendrik Schawe, Alexander K. Hartmann, Alexander Hartmann. Asymptotic behavior of the length of the longest increasing subsequences of random walks.

*Physical Review E*, American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032102⟩. ⟨hal-02512208⟩We numerically estimate the leading asymptotic behavior of the length $L_{n}$ of the longest increasing subsequence of random walks with step increments following Student's $t$-distribution with parameter in the range $1/2 \leq \nu \leq 5$. We find that the expected value $\mathbb{E}(L_{n}) \sim n^{\theta}\ln{n}$ with $\theta$ decreasing from $\theta(\nu=1/2) \approx 0.70$ to $\theta(\nu \geq 5/2) \approx 0.50$. For random walks with distribution of step increments of finite variance ($\nu > 2$), this confirms previous observation of $\mathbb{E}(L_{n}) \sim \sqrt{n}\ln{n}$ to leading order. We note that this asymptotic behavior (including the subleading term) resembles that of the largest part of random integer partitions under the uniform measure and that, curiously, both random variables seem to follow Gumbel statistics. We also provide more refined estimates for the asymptotic behavior of $\mathbb{E}(L_{n})$ for random walks with step increments of finite variance.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Oldenburg
- 3. Institut für Physik

## Archive ouverte HAL – Time Between the Maximum and the Minimum of a Stochastic Process

### Francesco Mori

^{1}Satya N. Majumdar^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Time Between the Maximum and the Minimum of a Stochastic Process.

*Physical Review Letters*, American Physical Society, 2019, 123 (20), ⟨10.1103/PhysRevLett.123.200201⟩. ⟨hal-02395492⟩We present an exact solution for the probability density function $P(\tau=t_{\min}-t_{\max}|T)$ of the time-difference between the minimum and the maximum of a one-dimensional Brownian motion of duration $T$. We then generalise our results to a Brownian bridge, i.e. a periodic Brownian motion of period $T$. We demonstrate that these results can be directly applied to study the position-difference between the minimal and the maximal height of a fluctuating $(1+1)$-dimensional Kardar-Parisi-Zhang interface on a substrate of size $L$, in its stationary state. We show that the Brownian motion result is universal and, asymptotically, holds for any discrete-time random walk with a finite jump variance. We also compute this distribution numerically for L\'evy flights and find that it differs from the Brownian motion result.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – A consistent quadratic curvature-tilt theory for fluid lipid membranes

### M. Mert Terzi

^{1}Muhammed Ergüder^{2}Markus Deserno^{2}#### M. Mert Terzi, Muhammed Ergüder, Markus Deserno. A consistent quadratic curvature-tilt theory for fluid lipid membranes.

*Journal of Chemical Physics*, American Institute of Physics, 2019, 151 (16), pp.164108. ⟨10.1063/1.5119683⟩. ⟨hal-02512290⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CMU - Carnegie Mellon University [Pittsburgh]