湮没分支布朗运动

Pub Date : 2024-05-09 DOI:10.1093/imrn/rnae068

Daniel Ahlberg, Omer Angel, Brett Kolesnik

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引用次数: 0

摘要

我们研究的是实线上由相互竞争的粒子组成的相互作用系统。正负粒子的两个种群按照分支布朗运动演化。当对立粒子相遇时，它们的电荷会中和，粒子会湮灭，就像惰性化学反应一样。我们的研究表明，在正概率的情况下，两个粒子群会共存，而且在这种情况下，界面是渐近线性的，具有随机斜率。我们还讨论了各种概括和悬而未决的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Annihilating Branching Brownian Motion

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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