Geodesic
Infinite Systems of Functional Equations and Gaussian Limiting Distributions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) (2012).

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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. 
@article{DMTCS_2012_special_262_a33,
     author = {Drmota, Michael and Gittenberger, Bernhard and Morgenbesser, Johannes F.},
     title = {Infinite {Systems} of {Functional} {Equations} and {Gaussian} {Limiting} {Distributions}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)},
     year = {2012},
     doi = {10.46298/dmtcs.3012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3012/}
}
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Drmota, Michael; Gittenberger, Bernhard; Morgenbesser, Johannes F. Infinite Systems of Functional Equations and Gaussian Limiting Distributions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) (2012). doi : 10.46298/dmtcs.3012. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3012/

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