相关论文: Rapid Mixing of Glauber Dynamics up to Uniqueness …
We study the hard-core model defined on independent sets of an input graph where the independent sets are weighted by a parameter $\lambda>0$. For constant $\Delta$, previous work of Weitz (2006) established an FPTAS for the partition…
We prove two results on the mixing times of Markov chains for two-spin systems. First, we show that the Glauber dynamics mixes in polynomial time for the Gibbs distributions of antiferromagnetic two-spin systems at the critical threshold of…
We give a complete characterization of the two-state anti-ferromagnetic spin systems which are of strong spatial mixing on general graphs. We show that a two-state anti-ferromagnetic spin system is of strong spatial mixing on all graphs of…
We prove an optimal $\Omega(n^{-1})$ lower bound on the spectral gap of Glauber dynamics for anti-ferromagnetic two-spin systems with $n$ vertices in the tree uniqueness regime. This spectral gap holds for all, including unbounded, maximum…
We prove Gibbs distribution of two-state spin systems(also known as binary Markov random fields) without hard constrains on a tree exhibits strong spatial mixing(also known as strong correlation decay), under the assumption that, for…
Given a graph $G$, the hard-core model defines a probability distribution over its independent sets, assigning to each set of size $k$ a probability of $\frac{\lambda^k}{Z}$, where $\lambda>0$ is a parameter known as the \emph{fugacity} and…
In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial approximation scheme for count- ing exponentially weighted independent sets (equivalently, approximating the partition function of the hard-core model from…
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…
Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006) establish a beautiful picture for the computational complexity of approximating the partition function of the hard-core…
We characterize the uniqueness condition in the hardcore model for bipartite graphs with degree bounds only on one side, and provide a nearly linear time sampling algorithm that works up to the uniqueness threshold. We show that the…
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 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…
We study complex zeros of the partition function of 2-spin systems, viewed as a multivariate polynomial in terms of the edge interaction parameters and the uniform external field. We obtain new zero-free regions in which all these…
We study the mixing time of Glauber dynamics on monotone systems. For monotone systems satisfying the entropic independence condition, we prove a new mixing time comparison result for Glauber dynamics. For concrete applications, we obtain…
We study the single-site Glauber dynamics for the fugacity $\lambda$, Hard-core model on the random graph $G(n, d/n)$. We show that for the typical instances of the random graph $G(n,d/n)$ and for fugacity $\lambda <…
Motivated by the community detection problem in Bayesian inference, as well as the recent explosion of interest in spin glasses from statistical physics, we study the classical Glauber dynamics for sampling from Ising models with sparse…
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…
A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D…
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…
The hard core model in statistical physics is a probability distribution on independent sets in a graph in which the weight of any independent set I is proportional to lambda^(|I|), where lambda > 0 is the vertex activity. We show that…