Rigorous mean-field limit and cross-diffusion

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 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...

Mean field limit for interacting particles

Rigorous Solution of a Mean Field Spin Glass Model

A separable spin glass model whose exchange integral takes the form Jij-J(ilj2+12jl) which was solved by van Hemmen et al. [12] using large deviation theory [14] is rigorously treated. The almost sure convergence criteria associated with the cumulant generating function C(t) with respect to the quenched random variables (is carefully investigated, and it is proved that the related excluded null...

Rigorous Analysis of Discontinuous Phase Transitions via Mean-field Bounds

We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice Z. Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition t...