Scaling limit for a second-order particle system with local annihilation

Abstract

For a second-order particle system in ${\mathbb{R}}^d$ subject to locally-in-space pairwise annihilation, we prove a scaling limit for its empirical measure on position and velocity towards a degenerate elliptic partial differential equation. Crucial ingredients are Green's function estimates for the associated hypoelliptic operator and an Itô-Tanaka trick.

arXiv comment26 pages