Infinite Systems of Functional Equations and Gaussian Limiting Distributions - Drmota, Michael; Gittenberger, Bernhard; Morgenbesser, Johannes F. (Discrete mathematics and theoretical computer science, 2012)
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.