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2016 Limiting distribution of the rightmost particle in catalytic branching Brownian motion
Sergey Bocharov, Simon C. Harris
Electron. Commun. Probab. 21: 1-12 (2016). DOI: 10.1214/16-ECP22

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 [10] for the degenerate case of catalytic branching.

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Sergey Bocharov. Simon C. Harris. "Limiting distribution of the rightmost particle in catalytic branching Brownian motion." Electron. Commun. Probab. 21 1 - 12, 2016. https://doi.org/10.1214/16-ECP22

Information

Received: 12 May 2016; Accepted: 7 September 2016; Published: 2016
First available in Project Euclid: 4 October 2016

zbMATH: 1346.60128
MathSciNet: MR3564217
Digital Object Identifier: 10.1214/16-ECP22

Subjects:
Primary: 60J55, 60J65, 60J80

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