Mixing Time and Simulated Annealing for the Stochastic Cellular Automata

Fukushima-Kimura, Bruno Hideki; Handa, Satoshi; Kamakura, Katsuhiro; Kamijima, Yoshinori; Kawamura, Kazushi; Sakai, Akira

Mixing Time and Simulated Annealing for the Stochastic Cellular Automata

Fukushima-Kimura, Bruno Hideki; Handa, Satoshi; Kamakura, Katsuhiro et al.

Journal of statistical physics, 2023, 190(4), 79

Permalink : https://hdl.handle.net/2115/90778

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https://arxiv.org/abs/2007.11287			1

論文情報

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アクセス権	metadata only access
URI	https://hdl.handle.net/2115/90778
タイトル	Mixing Time and Simulated Annealing for the Stochastic Cellular Automata
著者	Fukushima-Kimura, Bruno Hideki ; Handa, Satoshi ; Kamakura, Katsuhiro ; Kamijima, Yoshinori ; Kawamura, Kazushi ; Sakai, Akira
著者名 Fukushima-Kimura, Bruno Hideki
著者名 Handa, Satoshi
著者名 Kamakura, Katsuhiro
著者名 Kamijima, Yoshinori
著者名 Kawamura, Kazushi
e-Rad_Researcher 50506996 著者名 Sakai, Akira
言語	英語
キーワード	Probabilistic cellular automata
	stochastic cellular automata
	simulated annealing
	stochastic optimization
	parallel dynamics
	Markov chain Monte Carlo
	ground states of Ising model
	Ising model
発行日	2023
出版者	Springer
収録物名	Journal of statistical physics
巻(号)	190(4)
ページ	79
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Accepted Manuscript
PISSN	0022-4715
NCID	AA00707889
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1007/s10955-023-03090-x
関連情報 (isVersionOf)	URI https://arxiv.org/abs/2007.11287