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Quantitative hydrodynamics for a generalized contact model

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  • Amorim, Julian
  • Jara, Milton
  • Xiang, Yangrui

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.

Suggested Citation

  • Amorim, Julian & Jara, Milton & Xiang, Yangrui, 2025. "Quantitative hydrodynamics for a generalized contact model," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001218
    DOI: 10.1016/j.spa.2025.104680
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