Annihilating Branching Brownian Motion-Reference-Cited by-同舟云学术

Annihilating Branching Brownian Motion

Published:2024-05-08 Issue:13 Volume:2024 Page:10425-10448
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Ahlberg Daniel¹,Angel Omer²,Kolesnik Brett³

Affiliation:

1. Department of Mathematics , Stockholm University, SE-106 91 Stockholm , Sweden

2. Department of Mathematics , University of British Columbia, 121-1984 Mathematics Rd, Vancouver, BC V6T 1Z2 , Canada

3. Department of Statistics , University of Oxford, 24-29, St Giles', Oxford OX1 3LB , UK

Abstract

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.

Funder

Natural Sciences and Engineering Research Council of Canada

Swedish Research Council

Publisher

Oxford University Press (OUP)

Link

https://academic.oup.com/imrn/article-pdf/2024/13/10425/58378012/rnae068.pdf

Reference29 articles.

1. Existence and coexistence in first-passage percolation;Ahlberg,2021

2. Multi-colour competition with reinforcement;Ahlberg;Ann. Inst. Henri Poincaré Probab. Stat.

3. To fixate or not to fixate in two-type annihilating branching random walks;Ahlberg;Ann. Probab.,2021

4. Competition in growth and urns;Ahlberg;Random Structures Algorithms,2019

5. An ergodic theorem for the frontier of branching Brownian motion;Arguin;Electron. J. Probab.,2013