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Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
Mixing Time and Simulated Annealing for the Stochastic Cellular Automata
| Title: | Mixing Time and Simulated Annealing for the Stochastic Cellular Automata |
| Authors: | Fukushima-Kimura, Bruno Hideki Browse this author | | Handa, Satoshi Browse this author | | Kamakura, Katsuhiro Browse this author | | Kamijima, Yoshinori Browse this author | | Kawamura, Kazushi Browse this author | | Sakai, Akira Browse this author →KAKEN DB |
| Keywords: | Probabilistic cellular automata | | stochastic cellular automata | | simulated annealing | | stochastic optimization | | parallel dynamics | | Markov chain Monte Carlo | | ground states of Ising model | | Ising model |
| Issue Date: | 2023 |
| Publisher: | Springer |
| Journal Title: | Journal of statistical physics |
| Volume: | 190 |
| Issue: | 4 |
| Start Page: | 79 |
| Publisher DOI: | 10.1007/s10955-023-03090-x |
| Abstract: | Finding a ground state of a given Hamiltonian of an Ising model on a graph G = (V, E) is an important but hard problem. The standard approach for this kind of problem is the application of algorithms that rely on single-spin-flip Markov chain Monte Carlo methods, such as the simulated annealing based on Glauber or Metropolis dynamics. In this paper, we investigate a particular kind of stochastic cellular automata, in which all spins are updated independently and simultaneously. We prove that (i) if the temperature is fixed sufficiently high, then the mixing time is at most of order log |V |, and that (ii) if the temperature drops in time n as 1/ log n, then the limiting measure is uniformly distributed over the ground states. We also provide some simulations of the algorithms studied in this paper implemented on a GPU and show their superior performance compared to the conventional simulated annealing. |
| Publisher URI: | https://arxiv.org/abs/2007.11287 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/90778 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 坂井 哲
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