ASEP(q,j) converges to the KPZ equation

Abstract

We show that a generalized Asymmetric Exclusion Process called ASEP(q,j) introduced by Carinci, Giardina, Redig and Sasamoto converges to the Cole-Hopf solution to the KPZ equation under weak asymmetry scaling.

20 pages

References in corpus (12)

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• KPZ equation limit of higher-spin exclusion processes
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• Weakly asymmetric bridges and the KPZ equation
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• Lectures on singular stochastic PDEs
• A generalized Asymmetric Exclusion Process with $U_q({\mathfrak{sl}}_2)$ stochastic duality
• On the scaling limits of weakly asymmetric bridges
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Cited by in corpus (9)

• The KPZ Limit of ASEP with Boundary
• Weakly asymmetric bridges and the KPZ equation
• Energy solutions of KPZ are unique
• Self-duality of Markov processes and intertwining functions
• Open ASEP in the Weakly Asymmetric Regime
• On the scaling limits of weakly asymmetric bridges
• Martingale-driven approximations of singular stochastic PDEs
• Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits
• Large-scale limit of interface fluctuation models