2018
DOI: 10.48550/arxiv.1805.04227
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Cutoff for the Swendsen-Wang dynamics on the lattice

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Cited by 1 publication
(15 citation statements)
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“…The latter work is based on the observation that while in Glauber dynamics, in one step the spin at a vertex can only depend on its immediate neighbors, the state of a vertex in SW by definition depends on all the vertices inside an independent percolation cluster sampled at each time step. Thus in the subcritical regime, since the cluster diameters have exponential tails, one can expect the same approach to go through and indeed this is what is made rigorous in [25].…”
Section: 2mentioning
confidence: 69%
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“…The latter work is based on the observation that while in Glauber dynamics, in one step the spin at a vertex can only depend on its immediate neighbors, the state of a vertex in SW by definition depends on all the vertices inside an independent percolation cluster sampled at each time step. Thus in the subcritical regime, since the cluster diameters have exponential tails, one can expect the same approach to go through and indeed this is what is made rigorous in [25].…”
Section: 2mentioning
confidence: 69%
“…Subsequently in [21,22], the results of the above papers were refined by inventing the general Information percolation machinery. Furthermore in very recent work, [25] extended the above framework to prove cutoff results for the non-local SW dynamics for Potts models on the torus in any dimension for suitably high temperatures.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
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