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Branching Brownian motion seen from its tip. (English) Zbl 1284.60154
Authors’ abstract: It has been conjectured since the work of S. P. Lalley and T. Sellke [Ann. Probab. 15, 1052–1061 (1987; Zbl 0622.60085)] that branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an invariant point process. Very recently, it emerged that this can be proved in several different ways (see, e.g. [É. Brunet and B. Derrida, J. Stat. Phys. 143, No. 3, 420–446 (2011; Zbl 1219.82095); L.-P. Arguin et al., Ann. Appl. Probab. 22, No. 4, 1693–1711 (2012; Zbl 1255.60152); Probab. Theory Relat. Fields 157, No. 3–4, 535–574 (2013; Zbl 1286.60045)])). The structure of this extremal point process turns out to be a Poisson point process with exponential intensity in which each atom has been decorated by an independent copy of an auxiliary point process. The main goal of the present work is to give a complete description of the limit object via an explicit construction of this decoration point process. Another proof and description has been obtained independently by Arguin et al. [Zbl 1255.60152].

##### MSC:
 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60G70 Extreme value theory; extremal stochastic processes
##### Keywords:
point processes; random walk; quadratic branching mechanism
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##### References:
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