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

2024/12/21 by Daniel Marahrens, Marahrens, Daniel, Angeliki Menegaki +3 · 1 citation
Engineering · #Advanced Control Systems Optimization #Fault Detection and Control Systems

paper · pdf · doi:10.48550/arxiv.2412.16714

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 L¹ 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.

Cited by

• Hydrodynamic Limit of the Symmetric Zero-Range Process with Slow Boundary

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