Limit theorems for Jacobi ensembles with large parameters

Limit theorems for beta-Jacobi ensembles

For a β-Jacobi ensemble determined by parameters a1, a2 and n, under the restriction that the three parameters go to infinity with n and a1 being of small orders of a2, we obtain some limit theorems about the eigenvalues. In particular, we derive the asymptotic distributions for the largest and the smallest eigenvalues, the central limit theorems of the eigenvalues, and the limiting distributio...

Central Limit Theorems for Additive Tree Parameters

We call a tree parameter additive if it can be determined recursively as the sum of the parameter values of all branches, plus a certain toll function. In this paper, we prove central limit theorems for very general toll functions, provided that they are bounded and small on average. Simply generated families of trees are considered as well as Pólya trees, recursive trees and binary search tree...

Limit Theorems For Large Tandem Queueing

limit theorems for order parameters of the Gardner problem

Fluctuations of the order parameters of the Gardner model for any α < α c are studied. It is proved that they converge in distribution to a family of jointly Gaussian random variables.

Limit theorems for mergesort

Central and local limit theorems (including large deviations) are established for the number of comparisons used by the standard top-down recursive mergesort under the uniform permutation model. The method of proof utilizes Dirichlet series, Mellin transforms and standard analytic methods in probability theory.