## Electronic Communications in Probability

### Limiting distribution of the rightmost particle in catalytic branching Brownian motion

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 70, 12 pp.

Dates
Accepted: 7 September 2016
First available in Project Euclid: 4 October 2016

https://projecteuclid.org/euclid.ecp/1475601101

Digital Object Identifier
doi:10.1214/16-ECP22

Mathematical Reviews number (MathSciNet)
MR3564217

Zentralblatt MATH identifier
1346.60128

#### Citation

Bocharov, Sergey; Harris, Simon C. Limiting distribution of the rightmost particle in catalytic branching Brownian motion. Electron. Commun. Probab. 21 (2016), paper no. 70, 12 pp. doi:10.1214/16-ECP22. https://projecteuclid.org/euclid.ecp/1475601101

#### References

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