Upper Tail Bounds for Stationary KPZ Models

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-Janjigian-Seppailainen (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.

Automated summary

We provide a proof of an upper tail bound in two classes of stationary models in the KPZ universality class, which is of the correct order up to a constant factor in the exponent. The proof is based on an exponential identity derived by Rains for last passage percolation with exponential weights, and recently re-derived by Emrah-Janjigian-Seppailainen (EJS). Our proof follows a similar approach for both classes of models, utilizing only general properties of monotonicity and convexity, suggesting its applicability to other stationary models.