Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-23T10:02:48.927Z Has data issue: false hasContentIssue false
  • English
  • Français

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: zeitouni@ee.technion.ac.il.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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