Work

Hydrodynamic Limits and Non-equilibrium Fluctuations for the Symmetric Inclusion Process with Long Jumps

Year: 2025

Type: article

Abstract: We consider a d –dimensional symmetric inclusion process (SIP), where particles are allowed to jump arbitrarily far apart. We establish both the hydrodynamic limit and non-equilibrium fluctuations for the empirical measure of particles. With the help of self-duality and Mosco convergence of Dirichlet forms, we extend structural parallels between exclusion and inclusion dynamics from the short-range scenario to the long-range setting. The hydrodynamic equation for the symmetric inclusion process turns out to be of non-local type. At the level of fluctuations from the hydrodynamic limit, we demonstrate that the density fluctuation field converges to a time-dependent generalized Ornstein–Uhlenbeck process whose characteristics are again non-local.

Source: Annales Henri Poincaré

DOI: 10.1007/s00023-025-01611-w

Authors: Mario Ayala, Johannes Zimmer

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Technische Universität München, Army Research Office

OpenAlex ID: W4413184781