Stationary fluctuations for a multi-species zero range process with long jumps

Linjie Zhao

Stochastic Processes and their Applications, 2025, vol. 186, issue C

Abstract: We consider stationary fluctuations for the multi-species zero range process with long jumps in one dimension, where the underlying transition probability kernel is p(x)=c+|x|−1−α if x>0 and =c−|x|−1−α if x<0. Above, c±≥0,α>0 are parameters. We prove that for 0<α<3/2, the density fluctuation fields converge to the stationary solution of a coupled fractional Ornstein–Uhlenbeck process, and for α=3/2, the limit points are concentrated on stationary energy solutions of a coupled fractional Burgers equation.

Keywords: Coupled fractional Burgers equation; Long jumps; Multi-species zero range process; Stationary fluctuations (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104645

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