A universal cutoff phenomenon for mean-field exchange models

2025/06/15 by Pietro Caputo, Caputo, Pietro, Matteo Quattropani +3
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Probability (math.PR) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2506.12816

openalex publication_date 2025/06/15 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

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.

Citations

• Spectral gap of the KMP and other stochastic exchange models on arbitrary graphs
• Cutoff for non-negatively curved diffusions
• Repeated Block Averages: entropic time and mixing profiles
• Intertwining and propagation of mixtures for generalized KMP models and harmonic models
• Hidden temperature in the KMP model
• Repeated Averages on Graphs
• Hydrodynamic limit and cutoff for the biased adjacent walk on the simplex
• Cutoff for non-negatively curved Markov chains
• Rates of convergence to equilibrium for Potlatch and Smoothing processes
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• Random walk on sparse random digraphs
• Kac's Walk on n-sphere mixes in nlog n steps
• Kac's Program in Kinetic Theory
• Entropy and chaos in the Kac model
• Statistical physics of social dynamics

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