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Weakly asymmetric bridges and the KPZ equation

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Consider N particles evolving according to the simple exclusion process on a linear lattice of 2N sites, with jump rates p_N to the left and q_N to the right. We do not impose periodic boundary conditions (no flux at 1 and 2N). I will present a complete classification of the scaling limits of the static, dynamic at equilibrium and dynamic out of equilibrium according to the asymmetry p_N – q_N. In particular, for a precise regime of asymmetry, we will see that the fluctuations around the hydrodynamic limit are given by the KPZ equation on the line and restricted to a finite interval of time.

This talk is part of the Probability series.

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