Systematic scanning Glauber dynamics for the mean-field Ising model
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910690275491840 |
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| author | Jeon, Sanghak |
| author_facet | Jeon, Sanghak |
| contents | We study the mixing time of systematic scan Glauber dynamics Ising model on the complete graph. On the complete graph $K_n$, at each time, $k \leq n$ vertices are chosen uniformly random and are updated one by one according to the uniformly randomly chosen permutations over the $k$ vertices. We show that if $k = o(n^{1/3})$, the high temperature regime $β< 1$ exhibits cutoff phenomena. For critical temperature regime $β= 1$, We prove that the mixing time is of order $n^{3/2}k^{-1}$. For $β> 1$, we prove the mixing time is of order $nk^{-1}\log n$ under the restricted dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10127 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Systematic scanning Glauber dynamics for the mean-field Ising model Jeon, Sanghak Probability Mathematical Physics 60J10, 60C05, 60G42 We study the mixing time of systematic scan Glauber dynamics Ising model on the complete graph. On the complete graph $K_n$, at each time, $k \leq n$ vertices are chosen uniformly random and are updated one by one according to the uniformly randomly chosen permutations over the $k$ vertices. We show that if $k = o(n^{1/3})$, the high temperature regime $β< 1$ exhibits cutoff phenomena. For critical temperature regime $β= 1$, We prove that the mixing time is of order $n^{3/2}k^{-1}$. For $β> 1$, we prove the mixing time is of order $nk^{-1}\log n$ under the restricted dynamics. |
| title | Systematic scanning Glauber dynamics for the mean-field Ising model |
| topic | Probability Mathematical Physics 60J10, 60C05, 60G42 |
| url | https://arxiv.org/abs/2307.10127 |