An invariance principle for the stochastic heat equation

Authors

Mathew Joseph, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Stochastics and Partial Differential Equations: Analysis and Computations

Abstract

We approximate the white-noise driven stochastic heat equation by replacing the fractional Laplacian by the generator of a discrete time random walk on the one dimensional lattice, and approximating white noise by a collection of i.i.d. mean zero random variables. As a consequence, we give an alternative proof of the weak convergence of the scaled partition function of directed polymers in the intermediate disorder regime, to the stochastic heat equation; an advantage of the proof is that it gives the convergence of all moments.

First Page

690

Last Page

745

DOI

10.1007/s40072-018-0118-9

Publication Date

12-1-2018

Comments

All Open Access, Green

Recommended Citation

Joseph, Mathew, "An invariance principle for the stochastic heat equation" (2018). Journal Articles. 1112.
https://digitalcommons.isical.ac.in/journal-articles/1112