Average properties of random walks on Galton-Watson trees
Dayue Chen (1997)
Annales de l'I.H.P. Probabilités et statistiques
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Average properties of random walks on Galton-Watson trees
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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...