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Infinite Systems of Functional Equations and Gaussian Limiting Distributions

Abstract : In this paper infinite systems of functional equations in finitely or infinitely many random variables arising in combinatorial enumeration problems are studied. 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.
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Michael Drmota, Bernhard Gittenberger, Johannes F. Morgenbesser. Infinite Systems of Functional Equations and Gaussian Limiting Distributions. 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. pp.453-478, ⟨10.46298/dmtcs.3012⟩. ⟨hal-01197227⟩

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