Gibbs' Measures on Combinatorial Objects and the Central Limit Theorem for an Exponential Family of Random Trees
- 1 January 1987
- journal article
- research article
- Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences
- Vol. 1 (1) , 47-59
- https://doi.org/10.1017/s0269964800000279
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.Keywords
This publication has 13 references indexed in Scilit:
- A theorem on treesPublished by Cambridge University Press (CUP) ,2009
- Optimization by Simulated AnnealingScience, 1983
- Matching behaviour is asymptotically normalCombinatorica, 1981
- Hermite polynomials and a duality relation for matchings polynomialsCombinatorica, 1981
- On the theory of the matching polynomialJournal of Graph Theory, 1981
- Application of the Berry-Esséen inequality to combinatorial estimatesJournal of Combinatorial Theory, Series A, 1980
- Central and local limit theorems applied to asymptotic enumerationJournal of Combinatorial Theory, Series A, 1973
- Theory of monomer-dimer systemsCommunications in Mathematical Physics, 1972
- Stirling Behavior is Asymptotically NormalThe Annals of Mathematical Statistics, 1967
- Equation of State Calculations by Fast Computing MachinesThe Journal of Chemical Physics, 1953