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arXiv · 2506.12816

A universal cutoff phenomenon for mean-field exchange models

Pietro Caputo·Matteo Quattropani·Federico Sau
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Abstract

We study a broad class of high-dimensional mean-field exchange models, encompassing both noisy and singular dynamics, along with their dual processes. This includes a generalized version of the averaging process as well as some non-reversible extensions of classical exchange dynamics, such as the flat Kac model. Within a unified framework, we analyze convergence to stationarity from worst-case initial data in Wasserstein distance. Our main result establishes a universal cutoff phenomenon at an explicit mixing time, with a precise window and limiting Gaussian profile. The mixing time and profile are characterized in terms of the logarithm of the size-biased redistribution random variable, thus admitting a natural entropic interpretation.

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Pietro Caputo, Matteo Quattropani, Federico Sau. 2025-06-15. A universal cutoff phenomenon for mean-field exchange models. https://arxiv.org/abs/2506.12816

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