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Journal article
ON A MEMORY GAME AND PREFERENTIAL ATTACHMENT GRAPHS
Advances in applied probability, v 48(2), pp 585-609
01 Jun 2016
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
In their recent paper Velleman and Warrington (2013) analyzed the expected values of some of the parameters in a memory game; namely, the length of the game, the waiting time for the first match, and the number of lucky moves. In this paper we continue this direction of investigation and obtain the limiting distributions of those parameters. More specifically, we prove that when suitably normalized, these quantities converge in distribution to a normal, Rayleigh, and Poisson random variable, respectively. We also make a connection between the memory game and one of the models of preferential attachment graphs. In particular, as a by-product of our methods, we obtain the joint asymptotic normality of the degree counts in the preferential attachment graphs. Furthermore, we obtain simpler proofs (although without rate of convergence) of some of the results of Pekoz et al. (2014) on the joint limiting distributions of the degrees of the first few vertices in preferential attachment graphs. In order to prove that the length of the game is asymptotically normal, our main technical tool is a limit result for the joint distribution of the number of balls in a multitype generalized Polya urn model.
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Details
- Title
- ON A MEMORY GAME AND PREFERENTIAL ATTACHMENT GRAPHS
- Creators
- Huseyin Acan - Monash UniversityPawel Hitczenko - Drexel University
- Publication Details
- Advances in applied probability, v 48(2), pp 585-609
- Publisher
- Applied Probability Trust
- Number of pages
- 25
- Grant note
- 208766 / Simons Foundation
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000384819800015
- Scopus ID
- 2-s2.0-84976416962
- Other Identifier
- 991019168709904721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Statistics & Probability