Probability Theory and Related Fields

, Volume 157, Issue 1–2, pp 405–451 | Cite as

Branching Brownian motion seen from its tip

  • E. Aïdékon
  • J. BerestyckiEmail author
  • É. Brunet
  • Z. Shi


It has been conjectured since the work of Lalley and Sellke (Ann. Probab., 15, 1052–1061, 1987) 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. Brunet and Derrida, A branching random walk seen from the tip, 2010, Poissonian statistics in the extremal process of branching Brownian motion, 2010; Arguin et al., The extremal process of branching Brownian motion, 2011). 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. (The extremal process of branching Brownian motion, 2011).

Mathematics Subject Classification

60J80 60G70 



We wish to warmly thank two anonymous referees for their careful reading and fruitful suggestions. We also wish to express our gratitude to Louis-Pierre Arguin for a useful conversation and Henri Berestycki for the argument behind Remark 6.3.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • E. Aïdékon
    • 1
  • J. Berestycki
    • 2
    Email author
  • É. Brunet
    • 3
  • Z. Shi
    • 2
  1. 1.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenThe Netherlands
  2. 2.Laboratoire de Probabilités et Modèles AléatoiresCNRS UMR 7599, UPMC Université Paris 6 Paris Cedex 05France
  3. 3.Laboratoire de Physique Statistique, École Normale SupérieureUPMC Université Paris 6, Université Paris Diderot, CNRS ParisFrance

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