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Main Authors: Dirr, Nicolas, Wu, Zhengyan, Zimmer, Johannes
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.05089
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author Dirr, Nicolas
Wu, Zhengyan
Zimmer, Johannes
author_facet Dirr, Nicolas
Wu, Zhengyan
Zimmer, Johannes
contents We develop quantitative error estimates connecting microscopic fluctuation of interacting particle systems with the mobilities of their hydrodynamic limits. Focusing on the Symmetric Simple Exclusion Process and systems of independent Brownian particles, we provide explicit bounds for the discrepancy between the quadratic variation of fluctuation fields and the corresponding mobilities, in terms of time and spatial discretization parameters. In addition, we establish analogous error estimates for a class of fluctuating hydrodynamic stochastic PDEs with regularized coefficients. For stochastic PDEs with irregular square-root type coefficients, including Dean-Kawasaki type equations, we further identify the asymptotic behavior of the associated fluctuation structures within the framework of renormalized kinetic solutions. Our results provide quantitative insights into the relationship between microscopic fluctuation mechanisms and macroscopic mobilities, and contribute to a structured comparison between discrete particle systems and continuum fluctuating hydrodynamic descriptions.
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id arxiv_https___arxiv_org_abs_2603_05089
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publishDate 2026
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spellingShingle Quantitative Error Estimates for Learning Macroscopic Mobilities from Microscopic Fluctuations
Dirr, Nicolas
Wu, Zhengyan
Zimmer, Johannes
Probability
Numerical Analysis
We develop quantitative error estimates connecting microscopic fluctuation of interacting particle systems with the mobilities of their hydrodynamic limits. Focusing on the Symmetric Simple Exclusion Process and systems of independent Brownian particles, we provide explicit bounds for the discrepancy between the quadratic variation of fluctuation fields and the corresponding mobilities, in terms of time and spatial discretization parameters. In addition, we establish analogous error estimates for a class of fluctuating hydrodynamic stochastic PDEs with regularized coefficients. For stochastic PDEs with irregular square-root type coefficients, including Dean-Kawasaki type equations, we further identify the asymptotic behavior of the associated fluctuation structures within the framework of renormalized kinetic solutions. Our results provide quantitative insights into the relationship between microscopic fluctuation mechanisms and macroscopic mobilities, and contribute to a structured comparison between discrete particle systems and continuum fluctuating hydrodynamic descriptions.
title Quantitative Error Estimates for Learning Macroscopic Mobilities from Microscopic Fluctuations
topic Probability
Numerical Analysis
url https://arxiv.org/abs/2603.05089