Related papers: Mean-field limits for Consensus-Based Optimization…
In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we…
Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…
Mean field approximation is a powerful technique which has been used in many settings to study large-scale stochastic systems. In the case of two-timescale systems, the approximation is obtained by a combination of scaling arguments and the…
We propose an entanglement mean field theory inspired approach for dealing with interacting classical many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
In this paper we are discussing the question how a continuous quantum system can be simulated by mean field fluctuations of a finite number of qubits. On the kinematical side this leads to a convergence result which states that…
We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…
Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…
We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and…
We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of all constituting ions. One feature of active…
We establish an algebraic rate of convergence in the large number of players limit of the value functions of N-particle stochastic control problems towards the value function of the corresponding McKean-Vlasov problem also known as mean…
We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large…
Across science and engineering, mean-field methods have been a powerful and versatile approach for the analysis of systems of many interacting elements. However, common arguments used to characterize an infinite population limit can be…
We propose a mean-field particle Monte Carlo method for simulating the N-body Lindblad equation. We provide a convergence result showing that a system of interacting particles converges to the corresponding nonlinear Lindblad equation in…
Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle…
Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples \emph{coordinate} through shared population statistics to transport probability mass more…
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…