Instantaneous control of interacting particle systems in the mean-field limit

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 for interacting particles

Interacting particle systems: hydrodynamic limit versus high density limit

In this short survey we compare aspects of two different approaches for scaling limits of interacting particle systems, the hydrodynamic limit and the high density limit. We present some examples, comments and open problems on each approach for different scenarios: the law of large numbers, the central limit theorem, and the large deviations principle. It is given a special attention to a recen...

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...