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arXiv · 2412.16714

A consistency-stability approach to scaling limits of zero-range processes

Daniel Marahrens·Angeliki Menegaki·Clément Mouhot
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Abstract

We propose a simple quantitative method for studying the hydrodynamic limit of interacting particle systems on lattices. It is applied to the diffusive scaling of the symmetric Zero-Range Process (in dimensions one and two). The rate of convergence is estimated in a Monge-Kantorovich distance asymptotic to the L^1 stability estimate of Kruzkhov, as well as in relative entropy; and it is uniform in time. The method avoids the use of the so-called ``block estimates''. It is based on a modulated Monge-Kantorovich distance estimate and microscopic stability properties.

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Daniel Marahrens, Angeliki Menegaki, Clément Mouhot. 2024-12-21. A consistency-stability approach to scaling limits of zero-range processes. https://arxiv.org/abs/2412.16714

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