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Abstract: Consider a generalized Polya urn, which contains balls of different colours and which evolves by drawing a ball at random and then adding a set of balls depending on the drawn colour.
We study the asymptotic composition of the urn. In the irreducible case, the result depends crucially on the ratio between the two largest (real parts of) eigenvalues of a matrix describing the additions; if this ratio is at most 1/2, the asymptotic distribution is normal, but not otherwise. In reducible cases there are further possibilities, including stable and Mittag-Leffler limits.
Some applications to random trees will be included.
Colloquium - 16 Uhr s.t.
Abstract: I will present a theorem of Riordan about spanning subgraphs in the uniform random graph model G(n,m). While trying to avoid most of the technical details, I will sketch the main ideas and steps in the proof, and show an application: the threshold for the spanning d-dimensional cube.