Abstract Discovered by Aldous, Diaconis and Shahshahani in the context of card shuffling,
the cutoff phenomenon has since then been established for a variety of Markov chains …

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 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 …

In this article, we provide detailed analysis of the long-time behavior of the underdamped
Langevin dynamics. We first provide a necessary condition guaranteeing that the zero-noise …

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 …

The Glauber-Exclusion process is a superposition of a Glauber dynamics and the Symmetric
Simple Exclusion Process (SSEP) on the lattice. The model was shown to admit a reaction …

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 …

We introduce and analyze the $ S_k $ shuffle on $ N $ cards, a natural generalization of the
celebrated random adjacent transposition shuffle. In the $ S_k $ shuffle, we choose …

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 …

On a finite state space, an irreducible continuous-time Markov chain converges to its unique
stationary measure, or in other words, mixes. The convergence is often measured by the …