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- W2964295243 abstract "The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and random spanning trees, but its dynamics have so far largely resisted analysis. In this paper we study a natural non-local Markov chain known as the Chayes-Machta dynamics for the mean-field case of the random-cluster model, and identify a critical regime (lambda_s,lambda_S) of the model parameter lambda in which the dynamics undergoes an exponential slowdown. Namely, we prove that the mixing time is Theta(log n) if lambda is not in [lambda_s,lambda_S], and e^Omega(sqrt{n}) when lambda is in (lambda_s,lambda_S). These results hold for all values of the second model parameter q > 1. In addition, we prove that the local heat-bath dynamics undergoes a similar exponential slowdown in (lambda_s,lambda_S)." @default.
- W2964295243 created "2019-07-30" @default.
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- W2964295243 date "2015-08-01" @default.
- W2964295243 modified "2023-10-18" @default.
- W2964295243 title "Dynamics for the mean-field random-cluster model" @default.
- W2964295243 doi "https://doi.org/10.4230/lipics.approx-random.2015.528" @default.
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