1301.6521 (Eric Lucon et al.)

Mean field limit for disordered diffusions with singular interactions    [PDF]

Eric Lucon, Wilhelm Stannat

Motivated by consideration from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $R^m$ in the presence of a random environment and with spatial extension: each diffusion is attached to one site of the lattice $Z^d$ and the interaction between two diffusions is attenuated by a spatial weight that depends on their positions. For a general class of singular weights (including the case already considered in the physical literature when interactions obey to a power law of parameter $0<\alphaView original: http://arxiv.org/abs/1301.6521