Equilibrium fluctuations for totally asymmetric interacting particle systems

2022/01/06 by Kohei Hayashi, Hayashi, Kohei
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2201.01987

openalex publication_date 2022/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study equilibrium fluctuations for a class of totally asymmetric zero-range type interacting particle systems. As a main result, we show that density fluctuation of our process converges to the stationary energy solution of the stochastic Burgers equation. As a special case, microscopic system we consider here is related to q-totally asymmetric simple exclusion processes (q-TASEPs) and our scaling limit corresponds to letting the quantum parameter q to be one.

Related

• Fluctuations for stationary q-TASEP
• Stochastic Burgers equation from long range exclusion interactions
• Stochastic Burgers Equation via Energy Solutions from Non-Stationary Particle Systems
• An upper bound on the fluctuations of a second class particle
• Non-equilibrium Fluctuations of Interacting Particle Systems