The mean-field limit for particle systems with uniform full-rank constraints

Mean Field Limit for Stochastic Particle Systems

We review some classical and more recent results for the derivation of mean field equations from systems of many particles, focusing on the stochastic case where a large system of SDE’s leads to a McKean-Vlasov PDE as the number N of particles goes to infinity. Classical mean field limit results require that the interaction kernel be essentially Lipschitz. To handle more singular interaction ke...

Mean-field Limit versus Small-noise Limit for Some Interacting Particle Systems

In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. Such diffusions can be obtained by taking the hydrodymamic limit in a huge system of linear diffusions in interaction. In both cases, for the linear and the nonlinear processes, small-noise asymptotics have been emphasized by specific large deviation phenomenons. The natural question, theref...

Mean Field Limit Theorems for CDMA Systems

The introduction of third generation wireless systems provides the opportunity to develop a wide range of new mobile data services. Many of the proposed services (e.g. Voice over IP, streaming audio/video, and other multimedia) include data that require guarantees on throughput, delay, and probability of data loss. However, wireless links are inherently unreliable since the channel is subject t...

Uniform Convergence in some Limit Theorems for Multiple Particle Systems

For n particles di using throughout R or Rd let n t A A B t be the random measure that counts the number of particles in A at time t It is shown that for some basic models Brownian particles with or without branching and di usion with a simple interaction the processes f n t E n t p n t M C L R g n N converge in law uniformly in t Previous results consider only convergence in law uniform in t b...

Mean field limit for interacting particles