Related papers: On Uniform Propagation of Chaos
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
New quantitative propagation of chaos results for mean field diffusion are proved via local and global entropy estimates. In the first result we work on the torus and consider singular, divergence free interactions $K\in L^p$, $p>d$. We…
We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…
We present a universal view on diffusive behaviour in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behaviour (Brownian motion with drift) and weak chaos…
Many of today's most pressing issues require a more robust understanding of how information spreads in populations. Current models of information spread can be thought of as falling into one of two varieties: epidemiologically-inspired…
Coordination games describe social or economic interactions in which the adoption of a common strategy has a higher payoff. They are classically used to model the spread of conventions, behaviors, and technologies in societies. Here we…
We develop an effective theory of pulse propagation in a nonlinear {\it and} disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena…
We consider a $N$-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit $N \to \infty$, as following from the previous…
Known by many names and arising in many settings, the forced linear diffusion model is central to the modeling of power and influence within social networks (while also serving as the mechanistic justification for the widely used…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
Models of ordering dynamics allow to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to…
Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…
We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the…
This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide…
We investigate the interplay between coherent effects characteristic of the propagation of linear waves, the non-linear effects due to interactions, and the quantum manifestations of classical chaos due to geometrical confinement, as they…
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without…
This paper is devoted to the study of mean-field limit for systems of indistinguables particles undergoing collision processes. As formulated by Kac \cite{Kac1956} this limit is based on the {\em chaos propagation}, and we (1) prove and…
Spreading processes play an increasingly important role in modeling for diffusion networks, information propagation, marketing and opinion setting. We address the problem of learning of a spreading model such that the predictions generated…
We study the spread of a quantum-mechanical wavepacket in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations…
We develop a microscopic transport theory in a randomly driven fermionic model with and without linear potential. The operator dynamics arise from the competition between noisy and static couplings, leading to diffusion regardless of…