Work

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

Year: 2025

Type: article

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.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2025.104645

Author: Linjie Zhao

Institution: Huazhong University of Science and Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities, Fundamental Research Funds for Central Universities of the Central South University