Related papers: Propagation of chaos and large deviations in mean-…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…
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 prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk…
One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…
This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network,…
This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over a network consisting of multiple groups of individuals. Limiting behaviors of the network are characterized by analyzing the…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
We develop a limit theory for controlled path-dependent mean field stochastic partial differential equations (SPDEs) within the semigroup approach of Da Prato and Zabczyk. More precisely, we prove existence results for mean field limits and…
The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and…
Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…
We generalize the multilevel Monte Carlo (MLMC) method of Giles to the simulation of systems of particles that interact via a mean field. When the number of particles is large, these systems are described by a McKean-Vlasov process - a…
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,…
The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +$\infty$) being granted by the study performed in (Chevallier, 2015), the aim of…
Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of an online social…
We introduce a framework to prove propagation of chaos for interacting particle systems with singular, density-dependent interactions, a classical challenge in mean-field theory. Our approach is to define the dynamics implicitly via a…
We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an…
We study the behavior of untrained neural networks whose weights and biases are randomly distributed using mean field theory. We show the existence of depth scales that naturally limit the maximum depth of signal propagation through these…