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Aldous’ conjecture on a killed branching random walk

Yueyun Hu — 2010

Actes des rencontres du CIRM

Consider a branching random walk on the real line with an killing barrier at zero: starting from a nonnegative point, particles reproduce and move independently, but are killed when they touch the negative half-line. The population of the killed branching random walk dies out almost surely in both critical and subcritical cases, where by subcritical case we mean that the rightmost particle of the branching random walk without killing has a negative speed and by critical case when this speed is zero....

The spread of a catalytic branching random walk

Philippe CarmonaYueyun Hu — 2014

Annales de l'I.H.P. Probabilités et statistiques

We consider a catalytic branching random walk on that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position M n : For some constant α , M n n α almost surely on the set of infinite number of visits of the origin. Then we determine all possible limiting laws for M n - α n as n goes to infinity.

Asymptotics for the survival probability in a killed branching random walk

Nina GantertYueyun HuZhan Shi — 2011

Annales de l'I.H.P. Probabilités et statistiques

Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope − , where denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we prove that when → 0, this probability decays like exp{−(+o(1)) / 1/2}, where is a positive constant depending...

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