Timeline for Polynomial time mixing Markov chain for multimodal distribution
Current License: CC BY-SA 4.0
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| Sep 10, 2022 at 15:00 | history | edited | Nawaf Bou-Rabee | CC BY-SA 4.0 |
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| Sep 8, 2022 at 2:07 | comment | added | Nawaf Bou-Rabee | At extremely low temperatures, not aware of any local chain that can achieve a poly mixing time from an arbitrary start. As far as I can tell, the best known non-asymptotic result for a local chain (Glauber) is arxiv.org/pdf/0806.1906.pdf See Figure 1 for a nice visual showing a window of size $O(1/\sqrt{n})$ around the critical temperature such that the mixing time is poly. For chains based on global moves (notably Swendsen-Wang and Parallel Tempering), the results are mixed with some poly and others exp; see arxiv.org/abs/1702.05797 for a nice survey and result. | |
| Sep 7, 2022 at 20:10 | vote | accept | voila | ||
| Sep 7, 2022 at 19:51 | comment | added | voila | Thanks, that was helpful. I have studied your 2018 paper (Coupling and convergence for HMC). Are you aware of any chain for mean-field Ising model or Ising model on a bounded degree graph at low temperature for which the mixing time is polynomial? | |
| Sep 7, 2022 at 19:44 | history | edited | Nawaf Bou-Rabee | CC BY-SA 4.0 |
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| Sep 7, 2022 at 19:38 | history | edited | Nawaf Bou-Rabee | CC BY-SA 4.0 |
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| Sep 7, 2022 at 19:31 | history | answered | Nawaf Bou-Rabee | CC BY-SA 4.0 |