PROPAGATION OF CHAOS FOR A CLASS OF FIRST ORDER MODELS WITH SINGULAR MEAN FIELD INTERACTIONS
Journal article, 2019

Dynamical systems of N particles in R-D interacting by a singular pair potential of mean field type are considered. The systems are assumed to be of gradient type and the existence of a macroscopic limit in the many particle limit is established for a large class of singular interaction potentials in stochastic as well as deterministic settings. The main assumption on the potentials is an appropriate notion of quasi-convexity. When D = 1 the convergence result is sharp when applied to strongly singular repulsive interactions and for a general dimension D the result applies to attractive interactions with Lipschitz singular interaction potentials, leading to stochastic particle solutions to the corresponding macroscopic aggregation equations. The proof uses the theory of gradient flows in Wasserstein spaces of Ambrosio, Gigli, and Savare.

Wasserstein space

propagation of chaos

mean field limit

Author

Robert J. Berman

Chalmers, Mathematical Sciences

Magnus Onnheim

Chalmers, Mathematical Sciences

SIAM Journal on Mathematical Analysis

0036-1410 (ISSN) 1095-7154 (eISSN)

Vol. 51 1 159-196

Subject Categories

Other Physics Topics

Theoretical Chemistry

Mathematical Analysis

DOI

10.1137/18M1196662

More information

Latest update

7/26/2019