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The dominating colour of an infinite Pólya urn model
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.ORCID iD: 0000-0002-0592-1808
2016 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 3, 914-924 p.Article in journal (Refereed) Published
Abstract [en]

We study a Pólya-type urn model defined as follows. Start at time 0 with a single ball of some colour. Then, at each time n≥1, choose a ball from the urn uniformly at random. With probability ½<p<1, return the ball to the urn along with another ball of the same colour. With probability 1−p, recolour the ball to a new colour and then return it to the urn. This is equivalent to the supercritical case of a random graph model studied by Backhausz and Móri (2015), (2016) and Thörnblad (2015). We prove that, with probability 1, there is a dominating colour, in the sense that, after some random but finite time, there is a colour that always has the most number of balls. A crucial part of the proof is the analysis of an urn model with two colours, in which the observed ball is returned to the urn along with another ball of the same colour with probability p, and removed with probability 1−p. Our results here generalise a classical result about the Pólya urn model (which corresponds to p=1).

Place, publisher, year, edition, pages
2016. Vol. 53, no 3, 914-924 p.
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-274483DOI: 10.1017/jpr.2016.49ISI: 000386349900019OAI: oai:DiVA.org:uu-274483DiVA: diva2:896568
Available from: 2016-01-21 Created: 2016-01-21 Last updated: 2017-11-30Bibliographically approved
In thesis
1. Asymptotics of a Random Graph Model
Open this publication in new window or tab >>Asymptotics of a Random Graph Model
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
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32 p.
Series
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2016:3
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-273524 (URN)
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Supervisors
Available from: 2016-01-25 Created: 2016-01-15 Last updated: 2016-01-25Bibliographically approved

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Thörnblad, Erik

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