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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Dayue Chen (1997)
Annales de l'I.H.P. Probabilités et statistiques
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Harry Kesten (1986)
Annales de l'I.H.P. Probabilités et statistiques
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Ivan Kramosil (1987)
Kybernetika
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Nina Gantert, Yueyun Hu, Zhan Shi (2011)
Annales de l'I.H.P. Probabilités et statistiques
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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...
Rathie, P.N., Zörnig, P. (2003)
International Journal of Mathematics and Mathematical Sciences
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Yuval Peres, Oded Schramm, Jeffrey E. Steif (2009)
Annales de l'I.H.P. Probabilités et statistiques
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In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last decade. Here we focus on graphs which percolate at criticality, and investigate the dynamical sensitivity of the infinite cluster. We first give two examples of bounded degree graphs, one which percolates for all times at criticality and one which has...