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arXiv · 2312.03669

Annihilating branching Brownian motion

Daniel Ahlberg·Omer Angel·Brett Kolesnik
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Abstract

We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the particles annihilate, as in an inert chemical reaction. We show that, with positive probability, the two populations coexist and that, on this event, the interface is asymptotically linear with a random slope. A variety of generalizations and open problems are discussed.

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Daniel Ahlberg, Omer Angel, Brett Kolesnik. 2023-12-06. Annihilating branching Brownian motion. https://doi.org/10.1093/imrn%2Frnae068

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