Upper tail decay of KPZ models with Brownian initial conditions

TL;DR

This paper analyzes the upper tail decay of KPZ growth models with Brownian initial conditions, providing a rigorous proof of the right tail asymptotics of the distribution function, extending previous results.

Contribution

It offers a new rigorous proof of the right tail asymptotics for KPZ models with non-stationary initial conditions, based on a variational problem approach.

Findings

Derived the right tail asymptotic of the distribution function

Provided a rigorous proof extending previous results

Connected the distribution to a variational problem

Abstract

In this paper we consider the limiting distribution of KPZ growth models with random but not stationary initial conditions introduced in [Chhita-Ferrari-Spohn 2018]. The one-point distribution of the limit is given in terms of a variational problem. By directly studying it, we deduce the right tail asymptotic of the distribution function. This gives a rigorous proof and extends the results obtained in [Meerson-Schmidt 2017].