Related papers: Potts Model On Random Trees

We consider the general p-state Potts model on random networks with a given degree distribution (random Bethe lattices). We find the effect of the suppression of a first order phase transition in this model when the degree distribution of…

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…

Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…

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…

Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a new framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of…

Data in the form of graphs, or networks, arise naturally in a number of contexts; examples include social networks and biological networks. We are often faced with the availability of multiple graphs on a single set of nodes. In this…

The polymer model framework is a classical tool from statistical mechanics that has recently been used to obtain approximation algorithms for spin systems on classes of bounded-degree graphs; examples include the ferromagnetic Potts model…

An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be…

We consider the problem of sampling from the Potts model on random regular graphs. It is conjectured that sampling is possible when the temperature of the model is in the uniqueness regime of the regular tree, but positive algorithmic…

We consider the problem of sampling from the ferromagnetic Potts and random-cluster models on a general family of random graphs via the Glauber dynamics for the random-cluster model. The random-cluster model is parametrized by an edge…

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a…

We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…

Numerous approaches have been explored for graph clustering, including those which optimize a global criteria such as modularity. More recently, Graph Neural Networks (GNNs), which have produced state-of-the-art results in graph analysis…

We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit, to an analytic function of the monomer activity. We…

The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…

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…

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…

For a tree Markov random field non-reconstruction is said to hold if as the depth of the tree goes to infinity the information that a typical configuration at the leaves gives about the value at the root goes to zero. The distribution of…

Let $t$ be a rooted tree and $n_i(t)$ the number of nodes in $t$ having $i$ children. The degree sequence $(n_i(t),i\geq 0)$ of $t$ satisfies $\sum_{i\ge 0} n_i(t)=1+\sum_{i\ge 0} in_i(t)=|t|$, where $|t|$ denotes the number of nodes in…

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…