Pair correlation functions and limiting distributions of iterated cluster point processes

Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices

The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediate...

Estimation Variances for Estimators of Product Densities and Pair Correlation Functions of Planar Point Processes

Approximations of the estimation variances of kernel estimators of the pair correlation function and the product density of a planar Poisson process are given. Furthermore, a heuristic approximation of the estimation variance of an estimator of the pair correlation function of a "general" planar point process is suggested. All formulae have been tested by simulation experiments.

Limiting Distributions for Branching Processes

Extended admissible functions and Gaussian limiting distributions

We consider an extension of Hayman’s notion of admissibility to bivariate generating functions f(z, u) that have the property that the coefficients ank satisfy a central limit theorem. It is shown that these admissible functions have certain closure properties. Thus, there is a large class of functions for which it is possible to check this kind of admissibility automatically. This is realized ...

New Limiting Distributions for Bellman–harris Processes

We present a number of new solutions to an integral equation arising in the limiting theory of Bellman–Harris processes. The argument proceeds via straightforward analysis of Mellin transforms. We also derive a criterion for the analyticity of the Laplace transform of the limiting distribution on Re(u) ≥ −c for some c > 0.