Hydrodynamic limits and non-equilibrium fluctuations for the Symmetric Inclusion Process with long jumps

Mario Ayala; Johannes Zimmer

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arXiv · 2410.21933

Hydrodynamic limits and non-equilibrium fluctuations for the Symmetric Inclusion Process with long jumps

Mario Ayala·Johannes Zimmer

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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.

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Mario Ayala, Johannes Zimmer. 2024-10-29. Hydrodynamic limits and non-equilibrium fluctuations for the Symmetric Inclusion Process with long jumps. https://arxiv.org/abs/2410.21933

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