Related papers: Existence and Convergence of Interacting Particle …

We consider an infinite system of particles on the positive real line, initiated from a Poisson point process, which move according to Brownian motion up until the hitting time of a barrier. The barrier increases when it is hit, allowing…

We consider dynamics of the empirical measure of vertex neighborhood states of Markov interacting jump processes on sparse random graphs, in a suitable asymptotic limit as the graph size goes to infinity. Under the assumption of a certain…

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…

We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The…

Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit.…

We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by…

We address the issue of the proximity of interacting diffusion models on large graphs with a uniform degree property and a corresponding mean field model, i.e. a model on the complete graph with a suitably renormalized interaction…

We study a system consisting of $n$ particles, moving forward in jumps on the real line. Each particle can make both independent jumps, whose sizes have some distribution, or ``synchronization'' jumps, which allow it to join a randomly…

In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…

We study a model for microscopic segregation in a homogeneous system of particles moving on a one-dimensional lattice. Particles tend to separate from each other, and evolution ceases when at least one empty site is found between any two…

Understanding the topology of the state space has proven to be extremely efficient for dynamical systems with a continuous state space. On the other hand, for particle systems on finite simple graphs, it has not yet been subject to deep…

Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…

We demonstrate that quantum correlations can emerge from the statistical correlations of random discrete models, without an a priori assumption that the random models are quantum mechanical in nature, that is without considering…

We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e., two particles are interacting if and only if they are connected in the underlying…

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

We analyze site percolation on directed and undirected graphs with site-dependent open-site probabilities. We construct upper bounds on cluster susceptibilities, vertex connectivity functions, and the expected number of simple open cycles…

We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…

In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…

We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…