Upper tail decay of KPZ models with Brownian initial conditions

Ferrari, Patrik and Vető, Bálint (2021) Upper tail decay of KPZ models with Brownian initial conditions. Electronic Communications in Probability, 26 (15). pp. 1-14. ISSN 1083-589X, ESSN: 1083-589X

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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 by Chhita, Ferrari and Spohn. 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 by Meerson and Schmidt.

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