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Maximal displacement in the $d$-dimensional branching Brownian motion

Abstract : We consider a branching Brownian motion evolving in R d. We prove that the asymptotic behaviour of the maximal displacement is given by a first ballistic order, plus a logarithmic correction that increases with the dimension d. The proof is based on simple geometrical evidence. It leads to the interesting following side result: with high probability, for any d ≥ 2, individuals on the frontier of the process are close parents if and only if they are geographically close.
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Contributor : Bastien Mallein <>
Submitted on : Friday, May 27, 2016 - 11:02:33 AM
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Bastien Mallein. Maximal displacement in the $d$-dimensional branching Brownian motion. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2015, ⟨10.1214/ECP.v20-4216⟩. ⟨hal-01322443⟩



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