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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.02625 |
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| _version_ | 1866915347235340288 |
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| author | Padilla-Garza, David Peilen, Luke Thoma, Eric |
| author_facet | Padilla-Garza, David Peilen, Luke Thoma, Eric |
| contents | We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse temperature $β$ satisfies $N^{-1} \ll β\ll N^{-\frac{1}{2}}$, where $N$ is the number of particles. This expands the temperature regime for which convergence to a Poisson point process has been proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Emergence of a Poisson process in weakly interacting particle systems Padilla-Garza, David Peilen, Luke Thoma, Eric Probability We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse temperature $β$ satisfies $N^{-1} \ll β\ll N^{-\frac{1}{2}}$, where $N$ is the number of particles. This expands the temperature regime for which convergence to a Poisson point process has been proved. |
| title | Emergence of a Poisson process in weakly interacting particle systems |
| topic | Probability |
| url | https://arxiv.org/abs/2405.02625 |