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arXiv · 2205.07312

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

Ruojun Huang
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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 It\^o-Tanaka trick.

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Ruojun Huang. 2022-05-15. Scaling limit for a second-order particle system with local annihilation. https://arxiv.org/abs/2205.07312

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