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Superexponential decay for the GEM process

Part of: Special processes Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

O. Zeitouni
O. Zeitouni*
Affiliation:
Technion-Israel Institute of Technology
*
∗Postal address: Department of Electrical Engineering, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel. Email address: [email protected].
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Abstract

We show that the GEM process has strong ordering properties: the probability that one of the k largest elements in the GEM sequence is beyond the first ck elements (c > 1) decays superexponentially in k.

Keywords

Large deviationsGEM process

MSC classification

Primary: 60F10: Large deviations
Secondary: 60G09: Exchangeability 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 776 - 781
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

This work was partly supported by a US-Israel BSF grant.

References

Dembo, A., and Zeitouni, O. (1993). Large Deviations Techniques and Applications. Jones and Bartlett, Boston, MA.Google Scholar
Pitman, J., and Yor, M. (1997). The two-parameter Poisson–Dirichlet distribution derived from a stable subordinator. Ann. Prob. 25, 855–900.Google Scholar