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November 1998 Large deviation principles for some random combinatorial structures in population genetics and Brownian motion
Shui Feng, Fred M. Hoppe
Ann. Appl. Probab. 8(4): 975-994 (November 1998). DOI: 10.1214/aoap/1028903371

Abstract

Large deviation principles are established for some random combinatorial structures including the Ewens sampling formula and the Pitman sampling formula. A path-level large deviation principle is established for the former on the cadlag space D$(o, 1], R)$ equipped with the uniform convergence topology, and the rate function is the same as for a Poisson process justifying the Poisson process approximation for the Ewens sampling formula at the large deviation level. A large deviation principle for the total number of parts in a partition is obtained for the Pitman formula; here the rate function depends only on one of the two parameters which display the different roles of the two parameters at different scales. In addition to these large deviation results, we also provide an embedding scheme which gives the Pitman sampling formula. A product of this embedding is an intuitive alternate proof of a result of Pitman on the limiting total number of parts.

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Shui Feng. Fred M. Hoppe. "Large deviation principles for some random combinatorial structures in population genetics and Brownian motion." Ann. Appl. Probab. 8 (4) 975 - 994, November 1998. https://doi.org/10.1214/aoap/1028903371

Information

Published: November 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0945.60019
MathSciNet: MR1661315
Digital Object Identifier: 10.1214/aoap/1028903371

Subjects:
Primary: 60F10
Secondary: 05A17 , 92D10

Keywords: Ewens sampling formula , large deviation principle , Pitman sampling formula , Population genetics , Random partitions

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 4 • November 1998
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