Intermediate disorder for directed polymers with space-time correlations

Fuente: arXiv
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Auteur principal: Parekh, Shalin
Format: Preprint
Publié: 2025
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author Parekh, Shalin
author_facet Parekh, Shalin
contents We revisit a result of Hairer-Shen on polymer-type approximations for the stochastic heat equation with a multiplicative noise (SHE) in $d=1$. We consider a general class of polymer models with strongly mixing environment in space and time, and we prove convergence to the Itô solution of the SHE (modulo shear). The environment is not assumed to be Gaussian, nor is it assumed to be white-in-time. Instead of using regularity structures or paracontrolled products, we rely on simpler moment-based characterizations of the SHE to prove the convergence. However, the price to pay is that our topology of convergence is weak.
format Preprint
id arxiv_https___arxiv_org_abs_2503_17888
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Intermediate disorder for directed polymers with space-time correlations
Parekh, Shalin
Probability
We revisit a result of Hairer-Shen on polymer-type approximations for the stochastic heat equation with a multiplicative noise (SHE) in $d=1$. We consider a general class of polymer models with strongly mixing environment in space and time, and we prove convergence to the Itô solution of the SHE (modulo shear). The environment is not assumed to be Gaussian, nor is it assumed to be white-in-time. Instead of using regularity structures or paracontrolled products, we rely on simpler moment-based characterizations of the SHE to prove the convergence. However, the price to pay is that our topology of convergence is weak.
title Intermediate disorder for directed polymers with space-time correlations
topic Probability
url https://arxiv.org/abs/2503.17888