Related papers: Local weak convergence for sparse networks of inte…
Using the theory of $L^p$-graphons (Borgs et al, 2014), we derive and rigorously justify the continuum limit for systems of differential equations on sparse random graphs. Specifically, we show that the solutions of the initial value…
A graph $G$ is weakly $\gamma$-closed if every induced subgraph of $G$ contains one vertex $v$ such that for each non-neighbor $u$ of $v$ it holds that $|N(u)\cap N(v)|<\gamma$. The weak closure $\gamma(G)$ of a graph, recently introduced…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
Local convergence has emerged as a fundamental tool for analyzing sparse random graph models. We introduce a new notion of local convergence, color convergence, based on the Weisfeiler-Leman algorithm. Color convergence fully characterizes…
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
Consider a discrete locally finite subset $\Gamma$ of $R^d$ and the complete graph $(\Gamma,E)$, with vertices $\Gamma$ and edges $E$. We consider Gibbs measures on the set of sub-graphs with vertices $\Gamma$ and edges $E'\subset E$. The…
The cluster state acquired by evolving the nearest-neighbor (NN) Ising model from a completely separable state is the resource for measurement-based quantum computation. Instead of an NN system, a variable-range power law interacting Ising…
We study the problem of distributed hypothesis testing with a network of agents where some agents repeatedly gain access to information about the correct hypothesis. The group objective is to globally agree on a joint hypothesis that best…
In a recent paper, Caron and Fox suggest a probabilistic model for sparse graphs which are exchangeable when associating each vertex with a time parameter in $\mathbb{R}_+$. Here we show that by generalizing the classical definition of…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
We study the geometric ergodicity and the long time behavior of the Random Batch Method for interacting particle systems, which exhibits superior numerical performance in recent large-scale scientific computing experiments. We show that for…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses…