Limits of logarithmic combinatorial structures
Open Access
- 1 October 2000
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 28 (4) , 1620-1644
- https://doi.org/10.1214/aop/1019160500
Abstract
Under very mild conditions, we prove that the limiting behavior of the component counts in a decomposable logarithmic combinatorial structure conforms to a single, unified pattern, which includes functional central limit theorems, Erdös-Turán laws, Poisson–Dirichlet limits for the large components and Poisson approximation in total variation for the total number ofcomponents. Our approach is entirely probabilistic, and the conditions can readily be verified in practice.Keywords
This publication has 21 references indexed in Scilit:
- Limits of logarithmic combinatorial structuresThe Annals of Probability, 2000
- Order statistics for decomposable combinatorial structuresRandom Structures & Algorithms, 1994
- Independent Process Approximations for Random Combinatorial StructuresAdvances in Mathematics, 1994
- How random is the characteristic polynomial of a random matrix ?Mathematical Proceedings of the Cambridge Philosophical Society, 1993
- On random polynomials over finite fieldsMathematical Proceedings of the Cambridge Philosophical Society, 1993
- Gaussian limiting distributions for the number of components in combinatorial structuresJournal of Combinatorial Theory, Series A, 1990
- A functional central limit theorem for the Ewens sampling formulaJournal of Applied Probability, 1990
- A Functional Central Limit Theorem for Random MappingsThe Annals of Probability, 1989
- Random permutations and Brownian motionPacific Journal of Mathematics, 1985
- Distribution statistique de l'ordre d'un element du groupe symetriqueActa Mathematica Hungarica, 1985