Upper tail decay of KPZ models with Brownian initial conditions

Patrik L. Ferrari; Bálint Vető

doi:10.1214/21-ecp385

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arXiv · 2007.13496

Upper tail decay of KPZ models with Brownian initial conditions

Patrik L. Ferrari·Bálint Vető

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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].

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Patrik L. Ferrari, Bálint Vető. 2020-07-27. Upper tail decay of KPZ models with Brownian initial conditions. https://doi.org/10.1214/21-ecp385

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