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2020 KPZ equation tails for general initial data
Ivan Corwin, Promit Ghosal
Electron. J. Probab. 25(none): 1-38 (2020). DOI: 10.1214/20-EJP467

Abstract

We consider the upper and lower tail probabilities for the centered (by time$/24$) and scaled (according to KPZ time$^{1/3}$ scaling) one-point distribution of the Cole-Hopf solution of the KPZ equation when started with initial data drawn from a very general class. For the lower tail, we prove an upper bound which demonstrates a crossover from super-exponential decay with exponent $3$ in the shallow tail to an exponent $5/2$ in the deep tail. For the upper tail, we prove super-exponential decay bounds with exponent $3/2$ at all depths in the tail.

Citation

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Ivan Corwin. Promit Ghosal. "KPZ equation tails for general initial data." Electron. J. Probab. 25 1 - 38, 2020. https://doi.org/10.1214/20-EJP467

Information

Received: 19 July 2019; Accepted: 17 May 2020; Published: 2020
First available in Project Euclid: 20 June 2020

zbMATH: 07225520
MathSciNet: MR4115735
Digital Object Identifier: 10.1214/20-EJP467

Subjects:
Primary: 60K35

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