Asymptotes of macroscopic observables in Gibbs measures of general interacting particle systems
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909648706076672 |
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| author | Padilla-Garza, David |
| author_facet | Padilla-Garza, David |
| contents | This paper studies the Gibbs measure of an interacting particle system with a general interaction kernel at various temperature regimes. We are particularly interested in fine features of the convergence to the mean-field density as the number of particles tends to infinity. Our main results are concentration bounds, and estimates on the Laplace transform of fluctuations. The main technique is a regularization procedure for general interaction kernels, based on an associated parabolic flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00961 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotes of macroscopic observables in Gibbs measures of general interacting particle systems Padilla-Garza, David Probability This paper studies the Gibbs measure of an interacting particle system with a general interaction kernel at various temperature regimes. We are particularly interested in fine features of the convergence to the mean-field density as the number of particles tends to infinity. Our main results are concentration bounds, and estimates on the Laplace transform of fluctuations. The main technique is a regularization procedure for general interaction kernels, based on an associated parabolic flow. |
| title | Asymptotes of macroscopic observables in Gibbs measures of general interacting particle systems |
| topic | Probability |
| url | https://arxiv.org/abs/2309.00961 |