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For a second-order particle system in $\mathbb R^d$ subject tolocally-in-space pairwise annihilation, we prove a scaling limit for itsempirical measure on position and velocity towards a degenerate ellipticpartial differential equation. Crucial ingredients are Green's functionestimates for the associated hypoelliptic operator and an It\^o-Tanaka trick.

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