Displaying similar documents to “The longtime behavior of branching random walk in a catalytic medium.”

Scaling limit of the random walk among random traps on ℤd

Jean-Christophe Mourrat (2011)

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

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Attributing a positive value to each ∈ℤ, we investigate a nearest-neighbour random walk which is reversible for the measure with weights ( ), often known as “Bouchaud’s trap model.” We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that ≥5. We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof...

Conditional limit theorems for intermediately subcritical branching processes in random environment

V. I. Afanasyev, Ch. Böinghoff, G. Kersting, V. A. Vatutin (2014)

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

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For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition appears. In this paper we study the intermediately subcritical case, which constitutes the borderline within this phase transition. We study the asymptotic behavior of the survival probability. Next the size of the population and the shape of the...