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Gibbs' Measures on Combinatorial Objects and the Central Limit Theorem for an Exponential Family of Random Trees

Published online by Cambridge University Press:  27 July 2009

Michael Steele
Michael Steele
Affiliation:
Program in Engineering Statistics Princeton University Princeton, New Jersey
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Abstract

A model for random trees is given which provides an embedding of the uniform model into an exponential family whose natural parameter is the expected number of leaves. The model is proved to be analytically and computationally tractable. In particular, a central limit theorem (CLT) for the number of leaves of a random tree is given which extends and sharpens Rényi's CLT for the uniform model. The method used is general and is shown to provide tractable exponential families for a variety of combinatorial objects.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 1 , January 1987 , pp. 47 - 59
Copyright
Copyright © Cambridge University Press 1987

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