Related papers: Optimal coupling for mean field limits
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a network of mycelium is analyzed as representative case, and the…
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…
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 $\gamma$,…
We study heterogeneously interacting diffusive particle systems with mean-field type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration…
We study a leader-follower system of interacting particles subject to feedback control and derive its mean-field limits through a two-step passage: first to a micro-macro system coupling leader particles with a follower fluid, and then to a…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
We study particle systems with singular pairwise interactions and non-vanishing diffusion in the mean-field scaling. A classical approach to describing corrections to mean-field behavior is through the analysis of correlation functions. For…
A multi-scale meshfree particle method for macroscopic mean field approximations of generalized interacting particle models is developed and investigated. The method is working in a uniform way for large and small interaction radii. The…
This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…
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…
When particles interact via two-body short-range central potential wells, binding can occur for some critical values of the coupling constants. Using the envelope theory, upper bounds for critical coupling constants are computed for quantum…
Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…
This paper presents a novel way to approximate a distribution governing a system of coupled particles with a product of independent distributions. The approach is an extension of mean field theory that allows the independent distributions…
A mean field feedback artificial neural network algorithm is developed and explored for the set covering problem. A convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function. An approximate…
We introduce a new consensus based optimization (CBO) method where interacting particle system is driven by jump-diffusion stochastic differential equations. We study well-posedness of the particle system as well as of its mean-field limit.…
We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite…
We consider first-order conservative systems of particles with binary Coulomb interactions in the mean-field scaling regime in dimensions $d\geq 3$. We show that if at some time, the associated sequence of empirical measures converges in 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…
Equilibrium properties of long-range interacting systems on lattices are investigated. There was a conjecture by Cannas et. al. that the mean-field theory is exact for spin systems with non-additive long-range interactions. This is called…