%0 Journal Article
%T Linear Statistics of Point Processes via Orthogonal Polynomials
%A E. Ryckman
%J Mathematics
%D 2008
%I arXiv
%R 10.1007/s10955-008-9564-5
%X For arbitrary $\beta > 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $\beta$ ensembles. We identify the distribution of these statistics then prove a joint central limit theorem. In the circular case, similar statements have been proved using different methods by a number of authors. In the Jacobi case these results are new.
%U http://arxiv.org/abs/0805.3516v2