Soutenance de thèse: Xiangyu Cao

Disordered statistical physics in low dimensions: extremes, glass transition, and localization.

Xiangyu Cao

This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices.

In the first part devoted to logREMs, we show how to characterize their common properties and model–specific data. Then we develop their replica symmetry breaking treatment, which leads to the freezing scenario of their free energy distribution and the general description of their minima process, in terms of decorated Poisson pointcess, in. W lsr report a series of new applications of the Jack polynomi ls in the exact predictions of some observables in the circular model and its variants. Finally, we present the recentcessgress on the exact connection between logREMs and the Liouville conformal field theory.

The goal of the second part is to introduce and study a new class of banded random matrices, the broadly distributed class, which is characterid an effective sparsen in. W will first study a specific model of the class, the Beta Banded random matrices, inspired by an exact mapping to a recently studied statistical model of long–range first–passage percolation/epidemics dynamics. Using analytical arguments based on the mapping and numerics, we show the existence of localization transitions with mobility edges in the « stretch–exponenti l » parameter–regime of the statistical models. Then, using a block–diagonalization renormalization approach, we argue that such localization transitions occur generically in the broadly distributed class.

The defense presentation will focus on the logREM–Liouville connection and the broadly distributed random matrices.

Directeurs de thèse: Alberto Rosso, Raoul Santachiara

Jury: Bertrand Georgeot, Jonathan Keating, Christopher Mudry, Didina Serban; invité: Pierre Le Doussal

Date/Time : 24/03/2017 - 14:00 - 15:30

Location : LPTMS-batimentc100, salle des conseils

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