Spectral Gap for the Stochastic Exchange Model
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908453432197120 |
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| author | Carlen, Eric A. Posta, Gustavo Tóth, Imre Péter |
| author_facet | Carlen, Eric A. Posta, Gustavo Tóth, Imre Péter |
| contents | We prove a spectral gap inequality for the stochastic exchange model studied by Gaspard and Gilbert and by Grigo, Khanin and Szász in connection with understanding heat conduction in a deterministic billiards model. The bound on the spectral gap that we prove is uniform in the number of particles, as had been conjectured. We adapt techniques that were originally developed to prove spectral gap bounds for the Kac model with hard sphere collisions, which, like the stochastic exchange model, has degenerate jump rates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_13533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Gap for the Stochastic Exchange Model Carlen, Eric A. Posta, Gustavo Tóth, Imre Péter Probability 60J25, 60J46, 45C05 We prove a spectral gap inequality for the stochastic exchange model studied by Gaspard and Gilbert and by Grigo, Khanin and Szász in connection with understanding heat conduction in a deterministic billiards model. The bound on the spectral gap that we prove is uniform in the number of particles, as had been conjectured. We adapt techniques that were originally developed to prove spectral gap bounds for the Kac model with hard sphere collisions, which, like the stochastic exchange model, has degenerate jump rates. |
| title | Spectral Gap for the Stochastic Exchange Model |
| topic | Probability 60J25, 60J46, 45C05 |
| url | https://arxiv.org/abs/2504.13533 |