Annihilating branching Brownian motion
Probability
2025-11-18 v2
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.
Cite
@article{arxiv.2312.03669,
title = {Annihilating branching Brownian motion},
author = {Daniel Ahlberg and Omer Angel and Brett Kolesnik},
journal= {arXiv preprint arXiv:2312.03669},
year = {2025}
}
Comments
Video summary: https://youtu.be/aOjQUqwUKhA. v2: final version, International Mathematics Research Notices, to appear, https://doi.org/10.1093/imrn/rnae068