Equilibrium fluctuations of the weakly asymmetric inclusion process
Simon Gabriel
Abstract
We prove that the stationary density fluctuation field of the one-dimensional weakly asymmetric simple inclusion process converges to the energy solution of the stochastic Burgers equation. The key technical ingredient is a second-order Boltzmann-Gibbs principle tailored to the microscopic current. As a consequence, we also obtain Ornstein-Uhlenbeck fluctuations for the symmetric inclusion process in a weakly condensing regime, a result of independent interest.
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