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arXiv · 2411.14236

Size of chaos for Gibbs measures of mean field interacting diffusions

Zhenjie Ren·Songbo Wang
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Abstract

We investigate Gibbs measures for diffusive particles interacting through a two-body mean field energy. By identifying a gradient structure for the conditional law, we derive sharp bounds on the size of chaos, providing a quantitative characterization of particle independence. To handle interaction forces that are unbounded at infinity, we study the concentration of measure phenomenon for Gibbs measures via a defective Talagrand inequality, which may hold independent interest. Our approach provides a unified framework for both the flat semi-convex and displacement convex cases. Additionally, we establish sharp chaos bounds for the quartic Curie-Weiss model in the sub-critical regime, demonstrating the generality of this method.

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Zhenjie Ren, Songbo Wang. 2024-11-21. Size of chaos for Gibbs measures of mean field interacting diffusions. https://doi.org/10.1007/s00440-025-01435-z

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