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Wed, 29 Jan 2014 15:36:28 +0100Wed, 29 Jan 2014 15:36:28 +0100On the Total External Length of the Kingman Coalescent
http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32892
We prove asymptotic normality of the total length of external branches in the Kingman coalescent. The proof uses an embedded Markov chain, which can be described as follows: Take an urn with black balls. Empty it step by step according to the rule: In each step remove a randomly chosen pair of balls and replace it by one red ball. Finally remove the last remaining ball. Then the numbers of red balls form a Markov chain with an unexpected property: It is time-reversible.Svante Janson; Götz Kerstingarticlehttp://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32892Wed, 29 Jan 2014 15:36:28 +0100The longtime behavior of branching random walk in a catalytic medium
http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32890
Consider a countable collection of particles located on a countable group, performing a critical branching random walk where the branching rate of a particle is given by a random medium fluctuating both in space and time. Here we study the case where the time-space random medium (called catalyst) is also a critical branching random walk evolving autonomously while the local branching rate of the reactant process is proportional to the number of catalytic particles present at a site. The catalyst process and the reactant process typically have different underlying motions.Andreas Greven; Achim Klenke; Anton Wakolbingerarticlehttp://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32890Wed, 29 Jan 2014 14:03:52 +0100