Analytic Urns Philippe Flajolet
نویسندگان
چکیده
The talk1 describes an analytic approach to urn models of the Pólya type where an urn may contain balls of either of two colours. At each step, a ball is randomly drawn and replaced by balls of the two colours; a fixed 2× 2-matrix with constant row sum determines the replacement policy. The treatment starts from a partial differential equation associated with the model and bases itself on conformal mapping arguments coupled with singularity analysis techniques. This gives access to moments characterizations, Gaussian limits and large deviation results. In some specific and well-determined cases, the urn models admit explicit representations in terms of Weierstraß elliptic functions.
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