Convergence of ASEP to KPZ with basic coupling of the dynamics

Shalin Parekh

Stochastic Processes and their Applications, 2023, vol. 160, issue C, 351-370

Abstract: We prove an extension of a seminal result of Bertini and Giacomin. Namely we consider weakly asymmetric exclusion processes with several distinct initial data simultaneously. We run their dynamics according to a basic coupling, and we show joint convergence to the solution of the KPZ equation with the same driving noise in the limiting equation. Along the way, we analyze fine properties of nontrivially coupled solutions-in-law of KPZ-type equations.

Keywords: Interacting particle systems; Stochastic partial differential equations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.03.007

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