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Asymptotic normality of some Graph-Related statistics

Published online by Cambridge University Press:  14 July 2016

Pierre Baldi  and
Yosef Rinott
Pierre Baldi*
Affiliation:
University of California, San Diego
Yosef Rinott*
Affiliation:
Hebrew University
*
∗Postal address: Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA.
∗∗Postal address: Department of Statistics, Hebrew University, Jerusalem.
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Abstract

Petrovskaya and Leontovich (1982) proved a central limit theorem for sums of dependent random variables indexed by a graph. We apply this theorem to obtain asymptotic normality for the number of local maxima of a random function on certain graphs and for the number of edges having the same color at both endpoints in randomly colored graphs. We briefly motivate these problems, and conclude with a simple proof of the asymptotic normality of certain U-statistics.

Keywords

CENTRAL LIMIT THEOREMDEPENDENT VARIABLESMAXIMA OF RANDOM FUNCTIONSRANDOM COLORINGSU-STATISTICSNEURAL NETWORKS
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 171 - 175
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Work done while visiting the Department of Mathematics at UCSD.

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