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- Title
Branching Brownian motion seen from its tip.
- Authors
Aïdékon, E.; Berestycki, J.; Brunet, É.; Shi, Z.
- Abstract
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 ).
- Subjects
BRANCHING processes; WIENER processes; POINT processes; STATISTICS; INDEPENDENCE (Mathematics); PROOF theory
- Publication
Probability Theory & Related Fields, 2013, Vol 157, Issue 1/2, p405
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s00440-012-0461-0