For d≥ 2 and all q≥ q 0 (d) we give an efficient algorithm to approximately sample from the
q-state ferromagnetic Potts and random cluster models on the torus (ℤ/n ℤ) d for any inverse …

An important paradigm in the understanding of mixing times of Glauber dynamics for spin
systems is the correspondence between spatial mixing properties of the models and bounds …

We study dynamical aspects of the q‐state Potts model on an n× n box at its critical βc (q).
Heat‐bath Glauber dynamics and cluster dynamics such as Swendsen–Wang (that …

We consider the ferromagnetic q-state Potts model with zero external field in a finite volume
and assume that its stochastic evolution is described by a Glauber-type dynamics …

We establish rapid mixing of the random-cluster Glauber dynamics on random\varDelta Δ-
regular graphs for all q ≥ 1 q≥ 1 and p< p_u (q,\varDelta) p< pu (q, Δ), where the threshold …

The study of crossing probabilities-ie probabilities of existence of paths crossing rectangles-
has been at the heart of the theory of two-dimensional percolation since its beginning. They …

The random-cluster model is a unifying framework for studying random graphs, spin systems
and electrical networks that plays a fundamental role in designing efficient Markov Chain …

We consider the problem of sampling from the ferromagnetic Potts and random-cluster
models on a general family of random graphs via the Glauber dynamics for the random …

We consider the random‐cluster model (RCM) on with parameters p∈(0, 1) and q≥ 1. This
is a generalization of the standard bond percolation (with edges open independently with …

The random-cluster model with parameters (p,q) is a random graph model that generalizes
bond percolation (q=1) and the Ising and Potts models (q≧2). We study its Glauber …