Convergence in Law for the Branching Random Walk Seen from Its Tip
2015; Springer Science+Business Media; Volume: 30; Issue: 1 Linguagem: Inglês
10.1007/s10959-015-0636-6
ISSN1572-9230
Autores Tópico(s)Stochastic processes and financial applications
ResumoConsider 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).
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