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https://dx.doi.org/10.48550/ar...
Article . 2016
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Number of particles absorbed in a BBM on the extinction event

Authors: Corre, Pierre-Antoine;

Number of particles absorbed in a BBM on the extinction event

Abstract

We consider a branching Brownian motion which starts from $0$ with drift $��\in \mathbb{R}$ and we focus on the number $Z_x$ of particles killed at $-x$, where $x>0$. Let us call $��_0$ the critical drift such that there is a positive probability of survival if and only if $��>-��_0$. Maillard \cite{maillard2013number} and Berestycki et al. \cite{berestycki2015branching} have study $Z_x$ in the case $��\leq -��_0$ and $��\geq ��_0$ respectively. We complete the picture by considering the case where $��>-��_0$ on the extinction event. More precisely we study the asymptotic of $q_i(x):=\mathbb{P}\left(Z_x=i,��_x��_c$.

32 pages, 1 figure

Country
France
Keywords

branching Brownian motion with absorption, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Branching processes (Galton-Watson, birth-and-death, etc.), Probability (math.PR), FOS: Mathematics, Continuous-time Markov processes on general state spaces, Mathematics - Probability, F-KPPs

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green
gold