On the two-point function of the one-dimensional KPZ equation
Probability
2023-06-29 v3
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 an arbitrary two-sided Brownian motion, 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.
Cite
@article{arxiv.2208.14987,
title = {On the two-point function of the one-dimensional KPZ equation},
author = {Sergio I. López and Leandro P. R. Pimentel},
journal= {arXiv preprint arXiv:2208.14987},
year = {2023}
}
Comments
10 pages, 1 figure, typos corrected