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The Poisson boundary of random rational affinities

Sara Brofferio (2006)

Annales de l’institut Fourier

We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all p -adic fileds.

The spread of a catalytic branching random walk

Philippe Carmona, Yueyun 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.

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