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Velocity of the L-branching Brownian motion

Abstract : We consider a branching-selection system of particles on the real line that evolves according to the following rules: each particle moves according to a Brownian motion during an exponential lifetime and then splits into two new particles and, when a particle is at a distance L L of the highest particle, it dies without splitting. This model has been introduced by Brunet, Derrida, Mueller and Munier [10] in the physics literature and is called the L L -branching Brownian motion. We show that the position of the system grows linearly at a velocity vL v L almost surely and we compute the asymptotic behavior of vL v L as L L tends to infinity: vL=2‾√−π222‾√L2+o(1L2), v L 2 π 2 2 2 L 2 o 1 L 2 as conjectured in [10]. The proof makes use of results by Berestycki, Berestycki and Schweinsberg [5] concerning branching Brownian motion in a strip.
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Contributor : Serena Benassù <>
Submitted on : Friday, September 16, 2016 - 3:37:32 PM
Last modification on : Friday, March 27, 2020 - 4:00:57 AM


  • HAL Id : hal-01367717, version 1


Michel Pain. Velocity of the L-branching Brownian motion. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2016, 21, pp.28. ⟨hal-01367717⟩



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