Linear Statistics of Point Processes via Orthogonal Polynomials

Details Linear Statistics of Point Processes via Orthogonal Polynomials Linear Statistics of Point Processes via Orthogonal Polynomials

2008-05-22

arxiv.org/abs/0805.3516v2

Mathematics

Probability

Added references, corrected typos. To appear, J. Stat. Phys

Scientific paper

10.1007/s10955-008-9564-5

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.

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