Quantitative hydrodynamics for a generalized contact model

Julian Amorim, Milton Jara and Yangrui Xiang

Stochastic Processes and their Applications, 2025, vol. 188, issue C

Abstract: We derive a quantitative version of the hydrodynamic limit obtained in Chariker et al. (2023) for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the L2-speed of convergence of the empirical density of states in a generalized contact process defined over a d-dimensional torus of size n is of the optimal order O(nd/2). In addition, we show that the typical fluctuations around the aforementioned hydrodynamic limit are Gaussian, and governed by an inhomogeneous stochastic linear equation.

Date: 2025
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DOI: 10.1016/j.spa.2025.104680

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