Related papers: Mixing Time for the Solid-on-Solid Model

We investigate the Langevin dynamics for Wigner matrices with a spherical spike, in the regime where the signal-to-noise ratio $\theta$ is large, but order one. For large, order-$1$, signal-to-noise, the (worst-case) mixing time undergoes a…

The Swendsen-Wang dynamics is a Markov chain widely used by physicists to sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the complete graph K_n the mixing time of the chain is at…

We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature $\beta$ and random boundary conditions $\tau$ whose distribution P either stochastically dominates the extremal plus phase (hence the…

We analyze the mixing time of a class of oriented kinetically constrained spin models (KCMs) on a d-dimensional lattice of $n^d$ sites. A typical example is the North-East model, a 0-1 spin system on the two-dimensional integer lattice that…

Many finite-state reversible Markov chains can be naturally decomposed into "projection" and "restriction" chains. In this paper we provide bounds on the total variation mixing times of the original chain in terms of the mixing properties…

We prove rapid mixing for certain Markov chains on the set $S_n$ of permutations on $1,2,\dots,n$ in which adjacent transpositions are made with probabilities that depend on the items being transposed. Typically, when in state $\sigma$, a…

We prove that the continuous-time, single-flip Glauber dynamics for lozenge tilings of the size-$N$ hexagon mix in time $N^{2+o(1)}$. This was predicted to hold on fairly general domains of diameter $N$ (on the basis of the ``Lifshitz law''…

Let 0<\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \alpha of the state space.…

We address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on…

Consider a low temperature stochastic Ising model in the phase coexistence regime with Markov semigroup $P_t$. A fundamental and still largely open problem is the understanding of the long time behavior of $\d_\h P_t$ when the initial…

We give a new rapid mixing result for a natural random walk on the independent sets of a graph $G$. We show that when $G$ has bounded treewidth, this random walk -- known as the Glauber dynamics for the hardcore model -- mixes rapidly for…

We show that a new probabilistic technique, recently introduced by the first author, yields the sharpest bounds obtained to date on mixing times of Markov chains in terms of isoperimetric properties of the state space (also known as…

Consider random $d$-regular graphs, i.e., random graphs such that there are exactly $d$ edges from each vertex for some $d\ge 3$. We study both the configuration model version of this graph, which has occasional multi-edges and self-loops,…

We give a bound on the mixing time of a uniformly ergodic, reversible Markov chain in terms of the spectral radius of the transition operator. This bound has been established previously in finite state spaces, and is widely believed to hold…

A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of $k$-colorings of a graph $G$ on $n$ vertices with maximum degree $\Delta$ is rapidly mixing for $k\ge\Delta+2$. In FOCS 1999, Vigoda…

We consider spin systems on the integer lattice graph $\mathbb{Z}^d$ with nearest-neighbor interactions. We develop a combinatorial framework for establishing that exponential decay with distance of spin correlations, specifically the…

We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is…

We investigate the Glauber dynamics of the generalized (2+1)-dimensional $p$-SOS model under a hard floor constraint. This setting induces entropic repulsion: the integer-valued interface height is forced to remain above the wall and…

We introduce a new framework for analyzing Glauber dynamics for the Ising model. The traditional approach for obtaining sharp mixing results has been to appeal to estimates on spatial properties of the stationary measure from within a…

We consider spin systems with nearest-neighbor interactions on an $n$-vertex $d$-dimensional cube of the integer lattice graph $\mathbb{Z}^d$. We study the effects that exponential decay with distance of spin correlations, specifically the…