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Convergence in Law for the Branching Random Walk Seen from Its Tip

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  • Thomas Madaule

    (Université Paris XIII)

Abstract

Consider a critical branching random walk on the real line. In a recent paper, Aïdékon (2011) developed a powerful method to obtain the convergence in law of its minimum after a log-factor translation. By an adaptation of this method, we show that the point process formed by the branching random walk seen from the minimum converges in law to a decorated Poisson point process. This result, confirming a conjecture of Brunet and Derrida (J Stat Phys 143:420–446, 2011), can be viewed as a discrete analog of the corresponding results for the branching Brownian motion, previously established by Arguin et al. (2010, 2011) and Aïdékon et al. (2011).

Suggested Citation

  • Thomas Madaule, 2017. "Convergence in Law for the Branching Random Walk Seen from Its Tip," Journal of Theoretical Probability, Springer, vol. 30(1), pages 27-63, March.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:1:d:10.1007_s10959-015-0636-6
    DOI: 10.1007/s10959-015-0636-6
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    Cited by:

    1. Yan-Xia Ren & Ting Yang, 2024. "Limiting Distributions for a Class of Super-Brownian Motions with Spatially Dependent Branching Mechanisms," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2457-2507, September.
    2. Bandyopadhyay, Antar & Ghosh, Partha Pratim, 2023. "Right-most position of a last progeny modified time inhomogeneous branching random walk," Statistics & Probability Letters, Elsevier, vol. 193(C).

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