相关论文: The continuum limit of the Kuramoto model on spars…

We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics,…

Graphons are limit objects of sequences of graphs and are used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study signal processing on large graphs. A major limitation of this approach…

A sequence of graphs is FO-convergent if the probability of satisfaction of every first-order formula converges. A graph modeling is a graph, whose domain is a standard probability space, with the property that every definable set is Borel.…

This article develops limit laws for network sampling based estimates of subgraph counts and clustering coefficient of a large population network, and uses them for predictive inference. A model based approach is used, where the population…

Building upon the theory of graph limits and the Aldous-Hoover representation and inspired by Panchenko's work on asymptotic Gibbs measures (Annals of Probability 2013), we construct continuous embeddings of discrete probability…

We give a new $(1+\epsilon)$-approximation for sparsest cut problem on graphs where small sets expand significantly more than the sparsest cut (sets of size $n/r$ expand by a factor $\sqrt{\log n\log r}$ bigger, for some small $r$; this…

This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense…

We obtain the scaling limits of random graphs drawn uniformly in three families of intersection graphs: permutation graphs, circle graphs, and unit interval graphs. The two first families typically generate dense graphs, in these cases we…

Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…

We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution…

We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…

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…

We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…

Synchronization transition in oscillatory networks manifests itself as the appearance of a periodic global mode. While perfect in the thermodynamic limit, this mode fluctuates for finite ensembles. We characterize the coherence of this mode…

The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a…

We study topological and geometric functionals of $l_\infty$-random geometric graphs on the high-dimensional torus in a sparse regime, where the expected number of neighbors decays exponentially in the dimension. More precisely, we…

We consider two classes of natural stochastic processes on finite unlabeled graphs. These are Euclidean stochastic optimization algorithms on the adjacency matrix of weighted graphs and a modified version of the Metropolis MCMC algorithm on…

In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous…

In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is…

We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on graph classes with bounded expansion. This generalizes a result of Czygrinow et al.…