Two-time height distribution for 1D KPZ growth: the recent exact result and its tail via replica
Abstract
We consider the fluctuations in the stochastic growth of a one-dimensional interface of height described by the Kardar-Parisi-Zhang (KPZ) universality class. We study the joint probability distribution function (JPDF) of the interface heights at two times and , with droplet initial conditions at . In the limit of large times this JPDF is expected to become a universal function of the time ratio , and of the (properly scaled) heights and . Using the replica Bethe ansatz method for the KPZ equation, in [J. Stat. Mech. (2017) 053212] we obtained a formula for the JPDF in the (partial) tail regime where is large and positive, subsequently found in excellent agreement with experimental and numerical data [Phys. Rev. Lett. 118, 125701 (2017)]. Here we show that our results are in perfect agreement with Johansson's recent rigorous expression of the full JPDF [arXiv:1802.00729 ], thereby confirming the validity of our methods.
Keywords
Cite
@article{arxiv.1804.01948,
title = {Two-time height distribution for 1D KPZ growth: the recent exact result and its tail via replica},
author = {Jacopo de Nardis and Pierre Le Doussal},
journal= {arXiv preprint arXiv:1804.01948},
year = {2018}
}
Comments
18 pages, typos corrected