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- W3100832482 abstract "Consider a system of particles performing branching Brownian motion with negative drift $mu = sqrt{2 - epsilon}$ and killed upon hitting zero. Initially there is one particle at $x>0$. Kesten showed that the process survives with positive probability if and only if $epsilon>0$. Here we are interested in the asymptotics as $epsto 0$ of the survival probability $Q_mu(x)$. It is proved that if $L= pi/sqrt{epsilon}$ then for all $x in R$, $lim_{epsilon to 0} Q_mu(L+x) = theta(x) in (0,1)$ exists and is a travelling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when $x<L$ and $L-x to infty$. The proofs rely on probabilistic methods developed by the authors in a previous work. This completes earlier work by Harris, Harris and Kyprianou and confirms predictions made by Derrida and Simon, which were obtained using nonrigorous PDE methods." @default.
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- W3100832482 date "2011-01-01" @default.
- W3100832482 modified "2023-10-15" @default.
- W3100832482 title "Survival of near-critical branching Brownian motion" @default.
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