Related papers: Graph Limit for Interacting Particle Systems on We…
In this brief note, we report a formal mathematical observation: we are about to breach a major century-old barrier in the analysis of interacting particle systems. More precisely, it is well-known that in…
Most of the published articles on random motions have been devoted to the study of the telegraph process or its generalizations that describe the random motion in $R^n$ of a single particle in a Markov or semi-Markov medium. However, up to…
In many network problems, graphs may change by the addition of nodes, or the same problem may need to be solved in multiple similar graphs. This generates inefficiency, as analyses and systems that are not transferable have to be…
We study the behaviour of random labelled and unlabelled cographs with n vertices as n tends to infinity. Our main result is a novel probabilistic limit in the space of graphons.
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
Using the weak convergence approach to large deviations, we formulate and prove the large deviation principle (LDP) for W-random graphs in the cut-norm topology. This generalizes the LDP for Erd\H{o}s-R{\' e}nyi random graphs by Chatterjee…
We develop further the graph limit theory for dense weighted graph sequences. In particular, we consider probability graphons, which have recently appeared in graph limit theory as continuum representations of weighted graphs, and we…
We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…
In this paper, we consider a system of heterogeneously interacting quantum particles subject to indirect continuous measurement. The interaction is assumed to be of the mean-field type. We derive a new limiting quantum graphon system, prove…
This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…
In this paper, we study weakly interacting diffusion processes on random graphs. Our main focus is on the properties of the mean-field limit and, in particular, on the nonuniqueness and bifurcation structure of stationary states. By…
A graphon is a limiting object used to describe the behaviour of large networks through a function that captures the probability of edge formation between nodes. Although the merits of graphons to describe large and unlabelled networks are…
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…
The starting point of our analysis is a class of one-dimensional interacting particle systems with two species. The particles are confined to an interval and exert a nonlocal, repelling force on each other, resulting in a nontrivial…
Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…
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 consider a class of multi-particle reinforced interacting random walks. In this model, there are some (finite or infinite) particles performing random walks on a given (finite or infinite) connected graph, so that each particle has…
Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting…
Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…
We couple projective limits of probability measures to direct limits of their symmetry groups. We show that the direct limit group is the group of symmetries of the projective limit probability measure. If projective systems of probability…