Related papers: Optimal Mixing of Glauber Dynamics: Entropy Factor…

We show that the Jerrum-Sinclair Markov chain on matchings mixes in time $\widetilde{O}(\Delta^2 m)$ on any graph with $n$ vertices, $m$ edges, and maximum degree $\Delta$, for any constant edge weight $\lambda>0$. For general graphs with…

We prove an optimal $\Omega(n^{-1})$ lower bound for modified log-Sobolev (MLS) constant of the Glauber dynamics for anti-ferromagnetic two-spin systems with $n$ vertices in the tree uniqueness regime. Specifically, this optimal MLS bound…

We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to have partitions with linearly many pieces of bounded size, we…

We present a new lower bound on the spectral gap of the Glauber dynamics for the Gibbs distribution of a spectrally independent $q$-spin system on a graph $G = (V,E)$ with maximum degree $\Delta$. Notably, for several interesting examples,…

The mixing time of the Glauber dynamics for spin systems on trees is closely related to reconstruction problem. Martinelli, Sinclair and Weitz established this correspondence for a class of spin systems with soft constraints bounding the…

We consider the performance of Glauber dynamics for the random cluster model with real parameter $q>1$ and temperature $\beta>0$. Recent work by Helmuth, Jenssen and Perkins detailed the ordered/disordered transition of the model on random…

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 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…

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…

Spin-glasses are natural Gibbs distributions that have been studied in Theoretical CS for many decades. Recently, they have been gaining attention from the community as they emerge naturally in neural computation and learning, network…

Let $G = (V,E)$ be a graph on $n$ vertices and let $m^*(G)$ denote the size of a maximum matching in $G$. We show that for any $\delta > 0$ and for any $1 \leq k \leq (1-\delta)m^*(G)$, the down-up walk on matchings of size $k$ in $G$ mixes…

Gibbs sampling also known as Glauber dynamics is a popular technique for sampling high dimensional distributions defined on graphs. Of special interest is the behavior of Gibbs sampling on the Erd\H{o}s-R\'enyi random graph G(n,d/n). While…

A popular method for sampling from high-dimensional distributions is the \emph{Gibbs sampler}, which iteratively resamples sites from the conditional distribution of the desired measure given the values of the other coordinates. It is…

We study the ferromagnetic random field Ising model (RFIM) on a graph $G=(V,E)$ having maximal degree $\Delta$, where the external field at each vertex is an i.i.d. random variable. When the random field distribution is sufficiently…

We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising model on general graphs. We show that if \[(d-1)\tanh\beta<1,\] then there exists a constant C such that the discrete time mixing time of Gibbs…

We present novel results for fast mixing of Glauber dynamics using the newly introduced and powerful Spectral Independence method from [Anari, Liu, Oveis-Gharan: FOCS 2020]. We mainly focus on the Hard-core model and the Ising model. We…

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…

Two recent and seemingly-unrelated techniques for proving mixing bounds for Markov chains are: (i) the framework of Spectral Independence, introduced by Anari, Liu and Oveis Gharan, and its numerous extensions, which have given rise to…

We present novel results for fast mixing of Glauber dynamics using the newly introduced and powerful Spectral Independence method from [Anari, Liu, Oveis-Gharan: FOCS 2020]. In our results, the parameters of the Gibbs distribution are…

We show that the natural Glauber dynamics mixes rapidly and generates a random proper edge-coloring of a graph with maximum degree $\Delta$ whenever the number of colors is at least $q\geq (\frac{10}{3} + \epsilon)\Delta$, where…