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arXiv · 1603.01600

Limiting Distribution of the Rightmost Particle in Catalytic Branching Brownian Motion

Sergey Bocharov·Simon C. Harris
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Abstract

We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate $\beta \delta_0(\cdot)$, where $\delta_0(\cdot)$ is the Dirac delta function and $\beta$ is some positive constant. We show that the distribution of the rightmost particle centred about $\frac{\beta}{2}t$ 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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Sergey Bocharov, Simon C. Harris. 2016-03-04. Limiting Distribution of the Rightmost Particle in Catalytic Branching Brownian Motion. https://arxiv.org/abs/1603.01600

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