Large deviations for the height in 1D Kardar-Parisi-Zhang growth at late times
1 CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure - 24 rue Lhomond, 75231 Paris, France
2 LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay - 91405 Orsay, France
Received: 15 March 2016
Accepted: 29 March 2016
We study the atypically large deviations of the height 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.
PACS: 02.10.Yn – Matrix theory / 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2016