A power law of order 1/4 for critical mean field Swendsen-Wang dynamics (Q2925658)
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scientific article; zbMATH DE number 6357634
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A power law of order 1/4 for critical mean field Swendsen-Wang dynamics |
scientific article; zbMATH DE number 6357634 |
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17 October 2014
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Markov chains
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mixing time
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Ising model
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Swendsen-Wang algorithm
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math.PR
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A power law of order 1/4 for critical mean field Swendsen-Wang dynamics (English)
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Let a Swendsen-Wan Markov chain be given, defined on a complete graph on \(n\) vertices, and with percolation parametric \(cn^{-1}\), where \(c\) is a constant parameter independent of time. Then the mixing time of such a process is \(T=\Theta(\log\, n)\), when \(c>2\), \(T=\Theta {n^{1/4}}\), when \(c=2\), and \(T=\Theta (1)\), when \(c<2\). The proof of this result is lengthy and involves several estimates about percolation on a complete graph, and random graph estimates.
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