Abstract
In this paper we consider the limiting distribution of KPZ growth models with random but not stationary initial conditions introduced in [6]. 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 in [18].
Funding Statement
The work of P.L. Ferrari was partly funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – GZ 2047/1, projekt-id 390685813 and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Projektnummer 211504053 – SFB 1060. The work of B. Vető was supported by the NKFI (National Research, Development and Innovation Office) grants PD123994 and FK123962, by the Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the ÚNKP–20–5 New National Excellence Program of the Ministry for Innovation and Technology from the source of the National Research, Development and Innovation Fund.
Citation
Patrik L. Ferrari. Bálint Vető. "Upper tail decay of KPZ models with Brownian initial conditions." Electron. Commun. Probab. 26 1 - 14, 2021. https://doi.org/10.1214/21-ECP385
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