Related papers: Optimal coupling for mean field limits
The mutual compatibility of the dynamical equations and constraints describing a massive particle of arbitrary spin, though essential for consistency, is generically lost in the presence of interactions. The conventional Lagrangian approach…
The dynamics of non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The…
We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by…
In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…
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…
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given…
We formulate self-consistency equations for the distribution of links in spin models and of plaquettes in gauge theories. This improves upon known mean-field, mean-link, and mean-plaquette approximations in such that we self-consistently…
The diffraction patterns of crystalline materials with strongly-correlated disorder are characterised by the presence of structured diffuse scattering. Conventional analysis approaches generally seek to interpret this scattering either…
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
We investigate interacting phase oscillators whose mean field is at a different frequency from the mean or mode of their natural frequencies. The associated asymmetries lead to a macroscopic travelling wave. We show that the mean ensemble…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
The overview of the Exact Pairing technique based on the quasispin symmetry is presented. Extensions of this method are discussed in relation to mean field, quadrupole collectivity, electromagnetic transitions, and many-body level density.…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
The mean-field reaction-diffusion equations of the diffusive pair-annihilation and triplett-annihilation processes are considered. A direct lower bound on the time-dependent mean particle-density is derived. The results are applied to the…
A mean field approximation is employed to derive a master equation suitable for self-interacting baths and strong system-bath coupling. Solutions of the master equation are compared with exact solutions for a central spin interacting with a…
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…
We consider a $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…
It is a general fact that the coupling constant of an interacting many-body Hamiltonian do not correspond to any observable and one has to infer its value by an indirect measurement. For this purpose, quantum systems at criticality can be…