Kawasaki dynamics beyond the uniqueness threshold
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908497558372352 |
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| author | Bauerschmidt, Roland Bodineau, Thierry Dagallier, Benoit |
| author_facet | Bauerschmidt, Roland Bodineau, Thierry Dagallier, Benoit |
| contents | Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random $d$-regular graph mixes fast beyond the tree uniqueness threshold when $d$ is large enough (and conjecture that it mixes fast up to the tree reconstruction threshold for all $d\geq 3$). This result follows from a more general spectral condition for (modified) log-Sobolev inequalities for conservative dynamics of Ising models. The proof of this condition in fact extends to perturbations of distributions with log-concave generating polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04609 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kawasaki dynamics beyond the uniqueness threshold Bauerschmidt, Roland Bodineau, Thierry Dagallier, Benoit Probability Data Structures and Algorithms Mathematical Physics Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random $d$-regular graph mixes fast beyond the tree uniqueness threshold when $d$ is large enough (and conjecture that it mixes fast up to the tree reconstruction threshold for all $d\geq 3$). This result follows from a more general spectral condition for (modified) log-Sobolev inequalities for conservative dynamics of Ising models. The proof of this condition in fact extends to perturbations of distributions with log-concave generating polynomial. |
| title | Kawasaki dynamics beyond the uniqueness threshold |
| topic | Probability Data Structures and Algorithms Mathematical Physics |
| url | https://arxiv.org/abs/2310.04609 |