Related papers: Mean-field limit for particle systems with topolog…
We develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field limits and particle approximations, and we establish a…
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…
We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…
A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a…
A nonlinear Fokker-Planck equation is obtained in the continuous limit of a one-dimensional lattice with an energy landscape of wells and barriers. Interaction is possible among particles in the same energy well. A parameter $\gamma$,…
This paper concerns the derivation of the Kinetic Isothermal Euler system in dimension $d \geq 1$ from an N-particle system of extended charges with Coulomb interaction. This requires a combined mean field and quasineutral limit for a…
We consider Mckean-Vlasov type stochastic differential equations with multiplicative noise arising from the random vortex method. Such an equation can be viewed as the mean-field limit of interacting particle systems with singular…
In the limit of large particle numbers and low densities systems of cold atoms can be effectively described as macroscopic single particle systems in a mean-field approximation. In the case of a Bose-Hubbard system, modelling bosons on a…
The mean-field limit for the dynamics of bosons with random interactions is rigorously studied. It is shown that, for interactions that are almost-surely bounded, the many-body quantum evolution can be replaced in the mean-field limit by a…
In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. In some cases they correspond to processes attracted by their own probability distribution: the so-called self-stabilizing processes.…
We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction and diffusion functions from the path of one single particle in the system. Our estimator is obtained by…
Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…
We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to…
In this paper we study a general class of hybrid mathematical models of collective motions of cells under the influence of chemical stimuli. The models are hybrid in the sense that cells are discrete entities given by ODE, while the…
Motivated by several applications, including neuronal models, we consider the McKean-Vlasov limit for mean-field systems of interacting diffusions with simultaneous jumps. We prove propagation of chaos via a coupling technique that involves…
For a class of mean-field particle systems, we formulate a criterion in terms of the free energy that implies uniform bounds on the log-Sobolev constant of the associated Langevin dynamics. For certain double-well potentials with quadratic…
We rigorously justify the mean-field limit of a $N$-particle system subject to the Brownian motion and interacting through a Newtonian potential in $\mathbb{R}^3$. Our result leads to a derivation of the Vlasov-Poisson-Fokkker-Planck (VPFP)…
We consider the N-body Schr\"{o}dinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work \cite{AmNi}, the mean field limit is translated into a semiclassical problem with a…