Related papers: Mean field interaction on random graphs with dynam…
We prove limit theorems for systems of interacting diffusions on sparse graphs. For example, we deduce a hydrodynamic limit and the propagation of chaos property for the stochastic Kuramoto model with interactions determined by…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
We give a general existence and convergence result for interacting particle systems on locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state space to be Polish, and the jumps at a site to affect the…
Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the…
We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
A collection of $N$-diffusing interacting particles where each particle belongs to one of $K$ different populations is considered. Evolution equation for a particle from population $k$ depends on the $K$ empirical measures of particle…
The mean-field analysis of a multi-population agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markow-type jump process on the probability that each agent has of belonging to a given…
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…
We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…
This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…
Consider a system of homogeneous interacting diffusive particles labeled by the nodes of a unimodular Galton-Watson (UGW) tree, where the state of each node evolves like a d-dimensional diffusion whose drift coefficient depends on (the…
In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation…
The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…
We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the…
We consider a population of $N$ interacting neurons, represented by a multivariate Hawkes process: the firing rate of each neuron depends on the history of the connected neurons. Contrary to the mean-field framework where the interaction…
We study a model for flocking given by a $n$-particle system under which each particle jumps forward by a random amount, independently sampled from a given distribution $\theta$, with rate given by a non-increasing function $w$ of its…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…