Related papers: Quantitative convergence in relative entropy for a…
This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…
This note extends the modulated entropy and free energy methods for proving mean-field limits/propagation of chaos to the whole space without any confining potential, in contrast to previous work limited to the torus or requiring…
In this paper, the quantitative entropy-cost type propagation of chaos for mean field interacting particle system is obtained, where the interaction is only assumed to be bounded measurable and the initial distribution of a single particle…
The mean-field control problem for a multi-dimensional diffusion-aggregation system with Coulomb interaction (the so called parabolic elliptic Keller-Segel system) is considered. The existence of optimal control is proved through the…
We consider a drift-diffusion process of $N$ stochastic particles and show that its empirical measure converges, as $N\rightarrow \infty$, to the solution of the Landau equation. We work in the regime of very soft and Coulomb potentials…
This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate…
This paper deals with the diffusive limit of the Jin and Xin model and its approximation by an asymptotic preserving finite volume scheme. At the continuous level, we determine a convergence rate to the diffusive limit by means of a…
We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum…
Due to the regularization effect of the stochastic noise, the quantitative entropy-cost type propagation of chaos for mean field interacting particle system is proposed. The result shows that the Kac's chaotic property measured in relative…
The random batch method [J. Comput. Phys. 400 (2020) 108877] is not only an efficient algorithm for simulation of classical $N$-particle systems and their mean-field limit, but also a new model for interacting particle system that could be…
This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal…
Dynamical systems of N particles in \R^{D} interacting by a singular pair potential of mean field type are considered. The systems are assumed to be of gradient type and the existence of a macroscopic limit in the many particle limit is…
The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially…
We consider an open quantum system governed $N$-body Lindblad equation and study mean-field limits in this setting. We prove that the $N$-particle dynamics converges, in the sense of quantum relative entropy, to the tensorized solution of…
We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the…
We consider a class of interacting particle systems in continuous space of non-gradient type, which are reversible with respect to Poisson point processes with constant density. For these models, a rate of convergence was recently obtained…
In this work, we study the convergence of the empirical measure of moderately interacting particle systems with singular interaction kernels. First, we prove quantitative convergence of the time marginals of the empirical measure of…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
We consider deterministic particle dynamics with time evolving weights and their associated Kolmogorov equation and mean-field equation. We prove existence and unique- ness for the limit PDE alongside estimates on the growth of the…