KPZ equation tails for general initial data

DOI10.1214/20-EJP467zbMATH Open1456.60253arXiv1810.07129MaRDI QIDQ782809

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Publication date: 29 July 2020

Published in: (Search for Journal in Brave)

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 depth in the tail.

Full work available at URL: https://arxiv.org/abs/1810.07129

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