Survival probability of the branching random walk killed below a linear boundary

Jean Bérard (1) , Jean-Baptiste Gouéré (2)

1 ICJ - Institut Camille Jordan
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We give an alternative proof of a result by N. Gantert, Y. Hu and Z. Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary branching and bounded random walk steps. Connections with the Brunet-Derrida theory of stochastic fronts are discussed.

Domaines: Probabilités [math.PR]

Jean Bérard, Jean-Baptiste Gouéré. Survival probability of the branching random walk killed below a linear boundary. Electronic Journal of Probability, 2011, 16 (14), pp.396-418. ⟨hal-00433329v2⟩