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      Annihilating branching Brownian motion

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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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          Author and article information

          Journal
          06 December 2023
          Article
          2312.03669
          e19d81ac-ffc8-48e0-99b3-3a6f13480b08

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          60J65, 60J80
          Video summary: https://youtu.be/aOjQUqwUKhA
          math.PR

          Probability
          Probability

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