相关论文: Dobrushin conditions for systematic scan with bloc…
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…
Quantum Monte Carlo method with operator-loop update is a powerful technique that has been extensively used with great success in condensed matter physics. It enables one to sample from thermal and ground states of local Hamiltonians of…
We consider the computational task of sampling a bit string $x$ from a distribution $\pi(x)=|\langle x|\psi\rangle|^2$, where $\psi$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the…
Random walks on expanders play a crucial role in Markov Chain Monte Carlo algorithms, derandomization, graph theory, and distributed computing. A desirable property is that they are rapidly mixing, which is equivalent to having a spectral…
We study Markov chains for $\alpha$-orientations of plane graphs, these are orientations where the outdegree of each vertex is prescribed by the value of a given function $\alpha$. The set of $\alpha$-orientations of a plane graph has a…
We initiate the study of approximate maximum matching in the vertex partition model, for graphs subject to dynamic changes. We assume that the $n$ vertices of the graph are partitioned among $k$ players, who execute a distributed algorithm…
We present several results on the mixing time of the Glauber dynamics for sampling from the Gibbs distribution in the ferromagnetic Potts model. At a fixed temperature and interaction strength, we study the interplay between the maximum…
Single-site dynamics are canonical Markov chain based algorithms for sampling from high-dimensional distributions, such as the Gibbs distributions of graphical models. We introduce a simple and generic parallel algorithm that faithfully…
The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…
We present a Markov chain (Dikin walk) for sampling from a convex body equipped with a self-concordant barrier, whose mixing time from a "central point" is strongly polynomial in the description of the convex set. The mixing time of this…
We provide new upper bounds for mixing times of general finite Markov chains. We use these bounds to show that the total variation mixing time is robust under rough isometry for bounded degree graphs that are roughly isometric to trees.
The random-cluster model is a unifying framework for studying random graphs, spin systems and electrical networks that plays a fundamental role in designing efficient Markov Chain Monte Carlo (MCMC) sampling algorithms for the classical…
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…
The theory of rapid mixing random walks plays a fundamental role in the study of modern randomised algorithms. Usually, the mixing time is measured with respect to the worst initial position. It is well known that the presence of…
In this paper, we consider the Markov-Chain Monte Carlo (MCMC) approach for random sampling of combinatorial objects. The running time of such an algorithm depends on the total mixing time of the underlying Markov chain and is unknown in…
Exponential random graph models have become increasingly important in the study of modern networks ranging from social networks, economic networks, to biological networks. They seek to capture a wide variety of common network tendencies…
We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…
Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. Applications include Markov Chain Monte Carlo (MCMC) simulation and distributed scheduling for wireless networks. In…
In a series of recent works, Boyd, Diaconis, and their co-authors have introduced a semidefinite programming approach for computing the fastest mixing Markov chain on a graph of allowed transitions, given a target stationary distribution.…
We consider a dynamic random graph on $n$ vertices that is obtained by starting from a random graph generated according to the configuration model with a prescribed degree sequence and at each unit of time randomly rewiring a fraction…