A universal cutoff phenomenon for mean-field exchange models
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918059993726976 |
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| author | Caputo, Pietro Quattropani, Matteo Sau, Federico |
| author_facet | Caputo, Pietro Quattropani, Matteo Sau, Federico |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A universal cutoff phenomenon for mean-field exchange models Caputo, Pietro Quattropani, Matteo Sau, Federico Probability Mathematical Physics 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. |
| title | A universal cutoff phenomenon for mean-field exchange models |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2506.12816 |