Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 25 septembre 2012 à 14h00 en B107, Bernhard Gittenberger nous parlera de : Infinite-Dimensional Functional Equations and Gaussian Limiting Distributions

Résumé : What Philippe Flajolet popularized as the "Drmota-Lalley-Woods theorem" gives a kind generalisation of the Perron-Frobenius theory (rational world) to polynomial system of equations (algebraic world). It establishes a universal behaviour (square singularity, Gaussian limit law). This talk will deal with systems of functional equations in finitely or infinitely many random variables arising in combinatorial enumeration problems. We prove sufficient conditions under which the combinatorial random variables encoded in the generating function of the system tend to a finite or infinite dimensional limiting distribution. The proofs use a pinch of complex analysis and functional analysis. [Joint work with Michael Drmota and Johannes Morgenbesser]


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