相关论文: Mean-field limit and quantitative estimates with s…

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…

These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived as continuum versions of second order…

We introduce a method to numerically compute equilibrium measures for problems with attractive-repulsive power law kernels of the form $K(x-y) = \frac{|x-y|^\alpha}{\alpha}-\frac{|x-y|^\beta}{\beta}$ using recursively generated banded and…

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct…

This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion (e.g. driven by a fractional Laplacian) and a non-local singular convolution kernel. Each of those singular equations…

This paper is concerned with the mean-field limit for the gradient flow evolution of particle systems with pairwise Riesz interactions, as the number of particles tends to infinity. Based on a modulated energy method, using regularity and…

We obtain an upper bound on the heat kernel of the Keller-Segel finite particle system that exhibits blow up effects. The proof exploits a connection between Keller-Segel finite particles and certain non-local operators. The latter allows…

We consider the subcritical SQG equation in its natural scale invariant Sobolev space and prove the existence of a global attractor of optimal regularity. The proof is based on a new energy estimate in Sobolev spaces to bootstrap the…

This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…

We revisit the study published in [1], related to the behavior of 34 relativistic mean-field models, previously selected because they satisfy bulk nuclear matter properties, here used to compute the critical parameters of the symmetric…

In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale…

We study the regularity and large-time behavior of a crowd of species driven by chemo-tactic interactions. What distinguishes the different species is the way they interact with the rest of the crowd: the collective motion is driven by…

We consider a large number $N$ of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in…

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…

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…

Several differential equation models have been proposed to explain the formation of patterns characteristic of the grid cell network. Understanding the robustness of these patterns with respect to noise is one of the key open questions in…

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

We present a construction of a mean-field theory for thermodynamic and spectral properties of correlated electrons reliable in the strong-coupling limit. We introduce an effective interaction determined self-consistently from the reduced…

Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…

This paper generalizes and extends to the case of nonlinear effects and logistic perturbations some results recently developed in the literature where, for the linear counterpart and in absence of logistics, criteria toward boundedness for…