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MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics



Funded by The Danish National Research Foundation
Seminar
Tuesday, 11 November 2003, at 14:15 in KOL A4
Andreas Kyprianou
University of Utrecht
Charging balls with a branching Markov diffusion.

Abstract
Consider a branching diffusion in which each individual moves as a Markov diffusion with corresponding operator L and branches at a (spatial) rate b into precisely two particles at each fission point. Suppose the process begins from an individual particle. Given any ball and starting position, does a criteria exist which will guarantee the ball is visited (or charged) infinitely often by the branching process with positive/zero probability. The answer is yes and the criteria concerns the sign (+/-) of the minimum real number a such that there exist a positive harmonic function with respect to the operator (L+b-a). The number a is called the generalized principal eigenvalue. The proofs are purely probabilistic and conceptual, appealing to martingale techniques. This is joint work with Janos Englander.

Contact person:Goran Peskir.