Limiting Distribution of the Rightmost Particle in Catalytic Branching Brownian Motion

2016/03/04 by Sergey Bocharov, Simon C. Harris, Bocharov, Sergey +1
Business, Management and Accounting · Mathematics · Physics and Astronomy · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1603.01600

12 pages

arxiv created 2016/03/04 · openalex publication_date 2016/03/04 · arxiv updated 2016/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate βδ₀(⋅), where δ₀(⋅) is the Dirac delta function and β is some positive constant. We show that the distribution of the rightmost particle centred about \fracβ2t converges to a mixture of Gumbel distributions according to a martingale limit. Our results form a natural extension to S. Lalley and T. Sellke [6] for the degenerate case of catalytic branching.

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