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arXiv · 0805.3516

Linear Statistics of Point Processes via Orthogonal Polynomials

E. Ryckman
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Abstract

For arbitrary $β> 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $β$ 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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E. Ryckman. 2008-05-23. Linear Statistics of Point Processes via Orthogonal Polynomials. https://doi.org/10.1007/s10955-008-9564-5

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