Related papers: On Uniform Propagation of Chaos
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
This paper develops a non-asymptotic, local approach to quantitative propagation of chaos for a wide class of mean field diffusive dynamics. For a system of $n$ interacting particles, the relative entropy between the marginal law of $k$…
Diffusion models (DMs) excel in unconditional generation, as well as on applications such as image editing and restoration. The success of DMs lies in the iterative nature of diffusion: diffusion breaks down the complex process of mapping…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
Spreading processes on top of active dynamics provide a novel theoretical framework for capturing emerging collective behavior in living systems. I consider run-and-tumble dynamics coupled with coagulation/decoagulation reactions that lead…
In the particular case of a concave flux function, we are interested in the long time behaviour of the nonlinear process associated to the one-dimensional viscous scalar conservation law. We also consider the particle system obtained by…
A criterion for proving a strong form of propagation of chaos on the path space, known as entropy chaos, for a general interacting diffusion system is proposed. Our analysis focuses on the class of conservative diffusions introduced by…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics.…
Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean-Vlasov equation and a…
We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "normal form" coordinate system near such Turing patterns…
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 properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on i) the localization volume of a mode which defines the number of interacting partner modes, ii) the overlap…
A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this…
Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…
We consider the exit problem for small white noise perturbation of a smooth dynamical system on the plane in the neighborhood of a hyperbolic critical point. We show that if the distribution of the initial condition has a scaling limit then…
We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the exponential convergence of the mean field dynamics and then show…
Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. The…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…