Related papers: Mixing time of exponential random graphs
We present improved bounds for randomly sampling $k$-colorings of graphs with maximum degree $\Delta$; our results hold without any further assumptions on the graph. The Glauber dynamics is a simple single-site update Markov chain. Jerrum…
We study the random-cluster model on trees and treelike graphs at low temperatures. This is a model of dependent percolation parametrized by an edge probability $p\in (0,1)$ and a clustering weight $q\in [1,\infty)$, generalizing…
The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in enhancing phase space mixing of these protocols, thus…
Many complex systems change their structure over time, in these cases dynamic networks can provide a richer representation of such phenomena. As a consequence, many inference methods have been generalized to the dynamic case with the aim to…
The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the…
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…
Parallel tempering is a meta-algorithm for Markov Chain Monte Carlo that uses multiple chains to sample from tempered versions of the target distribution, enhancing mixing in multi-modal distributions that are challenging for traditional…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of…
In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state…
Folklore belief holds that metastable wells in low-temperature statistical mechanics models exhibit high-temperature behavior. We make this rigorous in the exponential random graph model (ERGM) through the lens of concentration of measure.…
We address the problem of sampling colorings of a graph $G$ by Markov chain simulation. For most of the article we restrict attention to proper $q$-colorings of a path on $n$ vertices (in statistical physics terms, the one-dimensional…
We consider Ising models on the hypercube with a general interaction matrix $J$, and give a polynomial time sampling algorithm when all but $O(1)$ eigenvalues of $J$ lie in an interval of length one, a situation which occurs in many models…
We consider sampling in the so-called low-temperature regime, which is typically characterised by non-local behaviour and strong global correlations. Canonical examples include sampling independent sets on bipartite graphs and sampling from…
In this article, we derive a sharp mixing time estimate of the Glauber dynamics for the Curie-Weiss-Potts model in the low-temperature regime. In contrast to the high-temperature regime studied by Cuff et al. (J. Stat. Phys. 149: 432-477,…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
Motivated by the `subgraphs world' view of the ferromagnetic Ising model, we develop a general approach to studying mixing times of Glauber dynamics based on subset expansion expressions for a class of graph polynomials. With a canonical…
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…
The spectral gap $\gamma$ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to…
Graph inference methods have recently attracted a great interest from the scientific community, due to the large value they bring in data interpretation and analysis. However, most of the available state-of-the-art methods focus on…