A BRANCHING PARTICLE SYSTEM AS A MODEL OF SEMIPUSHED FRONTS

• 成果类型: Article
• 署名作者: Tourniaire, Julie
• 署名单位: University of Vienna
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1691
• 发表日期: 2024
• 页码: 2104-2172
• 关键词: brownian-motion; fluctuations; coalescent; genealogy; selection; speed

摘要

We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift - mu and killed upon reaching 0, starting with N particles. More precisely, particles branch at rate rho /2 in the interval [ 0, 1], for some rho > 1, and at rate 1/2 in (1, +infinity ). The drift mu(rho) is chosen in such a way that, heuristically, the system is critical in some sense: the number of particles stays roughly constant before it eventually dies out. This particle system can be seen as an analytically tractable model for fluctuating fronts, describing the internal mechanisms driving the invasion of a habitat by a cooperating population. Recent studies from Birzu, Hallatschek and Korolev suggest the existence of three classes of fluctuating fronts: pulled, semipushed and fully pushed fronts. Here we rigorously verify and make precise this classification and focus on the semipushed regime. This complements previous results from Berestycki, Berestycki and Schweinsberg for the case rho = 1.