Large deviations for the height in 1D Kardar-Parisi-Zhang growth at late times

Pierre Le Doussal 1 Satya N. Majumdar 2 Gregory Schehr 2

EPL, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2016, 113, pp.60004

We study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the rate functions for the discrete single step growth model, as well as for the continuum KPZ equation in a droplet geometry. Based on our exact calculation of the rate functions we argue that models in the KPZ class undergo a third order phase transition from a strong coupling to a weak coupling phase, at late times.

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