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

Thomas Madaule ()
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Thomas Madaule: Université Paris XIII

Journal of Theoretical Probability, 2017, vol. 30, issue 1, 27-63

Abstract: 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).

Keywords: Branching random walk; Decorated Poisson point process; Convergence in law; 60J80; 60G55 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-015-0636-6

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