Asymptotic normality of some Graph-Related statistics
- 1 March 1989
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 26 (1), 171-175
- https://doi.org/10.2307/3214327
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
This publication has 12 references indexed in Scilit:
- A Multivariate Two-Sample Test Based on the Number of Nearest Neighbor Type CoincidencesThe Annals of Statistics, 1988
- Neural networks, orientations of the hypercube, and algebraic threshold functionsIEEE Transactions on Information Theory, 1988
- Normal Convergence by Higher Semiinvariants with Applications to Sums of Dependent Random Variables and Random GraphsThe Annals of Probability, 1988
- Multivariate Two-Sample Tests Based on Nearest NeighborsJournal of the American Statistical Association, 1986
- The simplest spin glassNuclear Physics B, 1984
- Random-energy model: An exactly solvable model of disordered systemsPhysical Review B, 1981
- Approximation Theorems of Mathematical StatisticsWiley Series in Probability and Statistics, 1980
- Random-Energy Model: Limit of a Family of Disordered ModelsPhysical Review Letters, 1980
- Multivariate Generalizations of the Wald-Wolfowitz and Smirnov Two-Sample TestsThe Annals of Statistics, 1979
- A Class of Statistics with Asymptotically Normal DistributionThe Annals of Mathematical Statistics, 1948