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Limiting Distribution of Particles Near the Frontier in the Catalytic Branching Brownian Motion

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Abstract

We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and in particular prove that the point process of particles travelling at the critical speed converges in distribution to a mixture of Poisson point processes.

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Notes

  1. lcscH = locally compact, second-countable Hausdorff topological space

  2. \(\mathcal{S}= \textit{Borel}\) subsets of \(S\). \(\hat{\mathcal{S}}=\textit{relatively}\) compact sets in \(\mathcal{S}\)

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Acknowledgements

We would like to thank the referees for their thorough reading of the manuscript and helpful suggestions. In particular, for pointing out a simpler proof of Theorem 1.

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  1. School of Mathematical Sciences, Zhejiang University, No. 38 Zheda Rd., Hangzhou, Zhejiang, 31002, P.R. China

    Sergey Bocharov

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  1. Sergey Bocharov
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Correspondence to Sergey Bocharov.

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The author is supported by NSFC grant (No. 11731012) and the Fundamental Research Funds for the Central Universities.

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Bocharov, S. Limiting Distribution of Particles Near the Frontier in the Catalytic Branching Brownian Motion. Acta Appl Math 169, 433–453 (2020). https://doi.org/10.1007/s10440-019-00305-w

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