Related papers: Mixing Time of Vertex-Weighted Exponential Random …

This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…

We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…

We consider Metropolis Glauber dynamics for sampling proper $q$-colourings of the $n$-vertex complete $b$-ary tree when $3\leq q\leq b/2\ln(b)$. We give both upper and lower bounds on the mixing time. For fixed $q$ and $b$, our upper bound…

In this paper we study the mixing time of the simple random walk on the giant component of supercritical $d$-dimensional random geometric graphs generated by the unit intensity Poisson Point Process in a $d$-dimensional cube of volume $n$.…

We study the sampling problem for simultaneous edge colorings. Given a pair of graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ which are on the same vertex set $V$, a simultaneous edge coloring is an edge coloring of $G_1\cup G_2$ so that each of…

Here we study the problem of sampling random proper colorings of a bounded degree graph. Let $k$ be the number of colors and let $d$ be the maximum degree. In 1999, Vigoda showed that the Glauber dynamics is rapidly mixing for any $k >…

Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. It has been used to analyze and design distributed CSMA (Carrier Sense Multiple Access) scheduling algorithms for…

Sampling from Gibbs distribution is a central problem in computer science as well as in statistical physics. In this work we focus on the k-colouring model} and the hard-core model with fugacity \lambda when the underlying graph is an…

The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…

Sampling graph colorings via local Markov chains is a central problem in approximate counting and Markov chain Monte Carlo (MCMC). We address the problem of sampling a random $k$-coloring of a graph with maximum degree $\Delta$. The…

Given a finite graph G, a vertex of the lamplighter graph consists of a zero-one labeling of the vertices of G, and a marked vertex of G. For transitive graphs G, we show that, up to constants, the relaxation time for simple random walk in…

For distributions over discrete product spaces $\prod_{i=1}^n \Omega_i'$, Glauber dynamics is a Markov chain that at each step, resamples a random coordinate conditioned on the other coordinates. We show that $k$-Glauber dynamics, which…

We study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with $n$ vertices and of bounded degree. We show that the relaxation time (defined as…

We study the mixing time of the single-site update Markov chain, known as the Glauber dynamics, for generating a random independent set of a tree. Our focus is obtaining optimal convergence results for arbitrary trees. We consider the more…

We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged.…

We present a simple combinatorial framework for establishing approximate tensorization of variance and entropy in the setting of spin systems (a.k.a. undirected graphical models) based on balanced separators of the underlying graph. Such…

The Glauber dynamics for the classical $2$-spin Curie-Weiss model on $N$ nodes with inverse temperature $\beta$ and zero external field is known to mix in time $\Theta(N\log N)$ for $\beta < \frac{1}{2}$, in time $\Theta(N^{3/2})$ at $\beta…

We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the…

We examine the problem of almost-uniform sampling proper $q$-colorings of a graph whose maximum degree is $\Delta$. A famous result, discovered independently by Jerrum(1995) and Salas and Sokal(1997), is that, assuming $q > (2+\delta)…

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,…