Convergence of finite-range weakly asymmetric exclusion processes on a circle

Convergence of finite-range weakly asymmetric exclusion processes on a circle

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Konstantin Matetski , University of Toronto
Fine Hall 110

We consider spatially periodic growth models built from weakly asymmetric exclusion processes with finite-range jumps and rates depending locally on configuration. We prove that at a large scale and after renormalization these processes converge to the Hopf-Cole solution of the KPZ equation driven by Gaussian space-time white noise. Since the driving noise of the discrete equation decorrelates slowly in time, the hydrodynamic behaviour of the system needs to be exploited.