相关论文: On the tractability of sampling from the Potts mod…

The random-cluster model with parameters $(p,q)$ is a random graph model that generalizes bond percolation ($q=1$) and the Ising and Potts models ($q\geq 2$). We study its Glauber dynamics on $n\times n$ boxes $\Lambda_{n}$ of the integer…

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…

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…

We investigate the ferromagnetic $q$-state Potts model on spherical Fibonacci graphs. These graphs are constructed by embedding quasi-uniform sites on a sphere and defining interactions via a chord-distance cutoff chosen to yield a network…

Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely…

We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…

Recent results establish for 2-spin antiferromagnetic systems that the computational complexity of approximating the partition function on graphs of maximum degree D undergoes a phase transition that coincides with the uniqueness phase…

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…

This paper studies a statistical network model generated by a large number of randomly sized overlapping communities, where any pair of nodes sharing a community is linked with probability $q$ via the community. In the special case with…

The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…

We study the $q$-state ferromagnetic Potts model on the $n$-vertex complete graph known as the mean-field (Curie-Weiss) model. We analyze the Swendsen-Wang algorithm which is a Markov chain that utilizes the random cluster representation…

We study the speed of convergence of the Swendsen-Wang (SW) dynamics for the $q$-state ferromagnetic Potts model on the $n$-vertex complete graph, known as the mean-field model. The SW dynamics was introduced as an attractive alternative to…

We prove a hardness of sampling result for the anti-ferromagnetic Ising model on random graphs of average degree $d$ for large constant $d$, proving that when the normalized inverse temperature satisfies $\beta>1$ (asymptotically…

Normal factor graph duality offers new possibilities for Monte Carlo algorithms in graphical models. Specifically, we consider the problem of estimating the partition function of the ferromagnetic Ising and Potts models by Monte Carlo…

The zero-temperature Glauber dynamics is used to investigate the persistence probability $P(t)$ in the Potts model with $Q=3,4,5,7,9,12,24,64, 128$, $256, 512, 1024,4096,16384 $,..., $2^{30}$ states on {\it directed} and {\it undirected}…

We study the thermodynamic properties of spin systems on small-world hypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin interactions onto a one-dimensional Ising chain with nearest-neighbor interactions. We use…

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analogue random-field Potts model corresponds to a multi-terminal…

We consider the ferromagnetic $q$-state Potts model with zero external field in a finite volume and assume that the stochastic evolution of this system is described by a Glauber-type dynamics parametrized by the inverse temperature $\beta$.…

We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and…

We prove sharpness of the phase transition for the random-cluster model with $q \geq 1$ on graphs of the form $\mathcal{S} := \mathcal{G} \times S$, where $\mathcal{G}$ is a planar lattice with mild symmetry assumptions, and $S$ a finite…