Abstract
In this short communication, we show that basic tools from Malliavin calculus can be applied to derive the two-point function of the slope of the one-dimensional KPZ equation, starting from a two-sided Brownian motion with an arbitrary diffusion parameter, in terms of the polymer end-point annealed distribution associated to the stochastic heat equation. We also prove that this distribution is given in terms of the derivative of the variance of the solution of the KPZ equation.
Funding Statement
Sergio I. López was supported by DGAPA–PAPIIT–UNAM grants PAPIIT IN-102822 and PASPA 2021-II. Leandro P. R. Pimentel was supported by the National Council of Scientific Researches (CNPQ, Brazil) Grant 305356/2019-4.
Citation
Sergio I. López. Leandro P. R. Pimentel. "On the two-point function of the one-dimensional KPZ equation." Braz. J. Probab. Stat. 37 (2) 455 - 462, June 2023. https://doi.org/10.1214/23-BJPS576
Information
