Convergence of ASEP to KPZ with basic coupling of the dynamics. (English) Zbl 1511.60148
Summary: We prove an extension of a seminal result of L. Bertini and G. Giacomin [Commun. Math. Phys. 183, No. 3, 571–607 (1997; Zbl 0874.60059)]. 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.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
Citations:
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