Nicolas Pouyanne
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Classification of large Pólya-Eggenberger urns with regard to their asymptotics
dmtcs:3384 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2005,
DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms
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https://doi.org/10.46298/dmtcs.3384
Classification of large Pólya-Eggenberger urns with regard to their asymptotics
Authors: Nicolas Pouyanne 1
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Nicolas Pouyanne
1 Laboratoire de Mathématiques de Versailles
This article deals with Pólya generalized urn models with constant balance in any dimension. It is based on the algebraic approach of Pouyanne (2005) and classifies urns having "large'' eigenvalues in five classes, depending on their almost sure asymptotics. These classes are described in terms of the spectrum of the urn's replacement matrix and examples of each case are treated. We study the cases of so-called cyclic urns in any dimension and $m$-ary search trees for $m \geq 27$.
Embedding of Urn Schemes into Continuous Time Markov Branching Processes and Related Limit Theorems
4 Documents citing this article
Source : OpenCitations
Chauvin, Brigitte; Liu, Quansheng; Pouyanne, Nicolas, 2014, Limit Distributions For Multitype Branching Processes Of $M$-Ary Search Trees, Annales De l'Institut Henri PoincarĂŠ, ProbabilitĂŠs Et Statistiques, 50, 2, 10.1214/12-aihp518.
Kuba, Markus, 2011, Analysis Of A Class Of Cannibal Urns, Electronic Communications In Probability, 16, none, 10.1214/ecp.v16-1669.
Meiners, Matthias; Mentemeier, Sebastian, 2016, Solutions To Complex Smoothing Equations, Probability Theory And Related Fields, 168, 1-2, pp. 199-268, 10.1007/s00440-016-0709-1.
MĂźller, Noela; Neininger, Ralph, 2018, Refined Asymptotics For The Composition Of Cyclic Urns, Electronic Journal Of Probability, 23, none, 10.1214/18-ejp243.