Spectral gap of the symmetric inclusion process
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917129521987584 |
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| author | Kim, Seonwoo Sau, Federico |
| author_facet | Kim, Seonwoo Sau, Federico |
| contents | We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on the same graph. In the regime in which the gamma-like reversible measures of the particle systems are log-concave, our bounds match, yielding a version for the symmetric inclusion process of the celebrated Aldous' spectral gap conjecture originally formulated for the interchange process. Finally, by means of duality techniques, we draw analogous conclusions for an interacting diffusion-like unbounded conservative spin system known as Brownian energy process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16607 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral gap of the symmetric inclusion process Kim, Seonwoo Sau, Federico Probability Mathematical Physics 60K35 We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on the same graph. In the regime in which the gamma-like reversible measures of the particle systems are log-concave, our bounds match, yielding a version for the symmetric inclusion process of the celebrated Aldous' spectral gap conjecture originally formulated for the interchange process. Finally, by means of duality techniques, we draw analogous conclusions for an interacting diffusion-like unbounded conservative spin system known as Brownian energy process. |
| title | Spectral gap of the symmetric inclusion process |
| topic | Probability Mathematical Physics 60K35 |
| url | https://arxiv.org/abs/2303.16607 |