Related papers: Quenched Random Graphs
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning…
The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured…
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…
Asymptotic properties of random regular graphs are object of extensive study in mathematics. In this note we argue, based on theory of spin glasses, that in random regular graphs the maximum cut size asymptotically equals the number of…
Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the…
Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…
The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…
Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the…
We explain the connection between the generalized spin quantities we have recently introduced and standard forms. We show how the calculation of various quantities of interest using these new forms is done. Focusing attention on expectation…
The critical behavior of a family of fully connected mean-field models with quenched disorder, the $M-p$ Ising spin glass, is analyzed, displaying a crossover between a continuous and a random first order phase transition as a control…
We present a new probabilistic modelling framework based on the recent notion of normal factor graph (NFG). We show that the proposed NFG models and their transformations unify some existing models such as factor graphs, convolutional…
We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization…
The majority-vote (MV) model is one of the simplest nonequilibrium Ising-like model that exhibits a continuous order-disorder phase transition at a critical noise. In this paper, we present a quenched mean-field theory for the dynamics of…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
A disordered system is denominated `annealed' when the interactions themselves may evolve and adjust their values to lower the free energy. The opposite (`quenched') situation when disorder is fixed, is the one relevant for physical…
In this paper we focus on comparing machine learning approaches for quantum graphs, which are metric graphs, i.e., graphs with dedicated edge lengths, and an associated differential operator. In our case the differential equation is a…
We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…