Derivation of the stochastic Burgers equation from totally asymmetric interacting particle systems

Kohei Hayashi

Stochastic Processes and their Applications, 2023, vol. 155, issue C, 180-201

Abstract: We consider equilibrium fluctuations for a class of totally asymmetric zero-range type interacting particle systems, which is particularly related to q-totally asymmetric simple exclusion processes (q-TASEPs). As a main result, we show that density fluctuation of our process converges to the stationary energy solution of the stochastic Burgers equation. Our proof is based on the second-order Boltzmann–Gibbs principle and a Taylor expansion argument.

Keywords: KPZ equation; Stochastic Burgers equation; Interacting particle systems; q-TASEP (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2022.10.006

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