Upper tail bounds for stationary KPZ models

TL;DR

This paper proves an upper tail bound for stationary KPZ models using an exponential identity, with a method applicable to various models in the KPZ universality class.

Contribution

It introduces a unified proof technique for upper tail bounds in stationary KPZ models based on monotonicity and convexity, extending applicability to many models.

Findings

Established upper tail bounds with correct order in stationary KPZ models.

The proof leverages exponential identities and general properties, simplifying previous approaches.

Method is adaptable to other stationary models in the KPZ class.

Abstract

We present a proof of an upper tail bound of the correct order (up to a constant factor in the exponent) in two classes of stationary models in the KPZ universality class. The proof is based on an exponential identity due to Rains in the case of Last Passage Percolation with exponential weights, and recently re-derived by Emrah-Jianjigian-Sepp\"ail\"ainen (EJS). Our proof follows very similar lines for the two classes of models we consider, using only general monotonocity and convexity properties, and can thus be expected to apply to many other stationary models.