Electronic Journal of Probability

KPZ equation tails for general initial data

Ivan Corwin and Promit Ghosal

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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.

Article information

Electron. J. Probab., Volume 25 (2020), paper no. 66, 38 pp.

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

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

KPZ equation KPZ line ensemble Brownian Gibbs property

Creative Commons Attribution 4.0 International License.


Corwin, Ivan; Ghosal, Promit. KPZ equation tails for general initial data. Electron. J. Probab. 25 (2020), paper no. 66, 38 pp. doi:10.1214/20-EJP467. https://projecteuclid.org/euclid.ejp/1592618468

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