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Linear Statistics of Point Processes via Orthogonal Polynomials

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Abstract

For arbitrary β>0, we use the orthogonal polynomials techniques developed in (Killip and Nenciu in arXiv:math/0508113v1, 2005; Killip and Nenciu in Int. Math. Res. Not. 50: 2665–2701, 2004) 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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  1. 253-37 Mathematics, California Institute of Technology, Pasadena, CA, 91125, USA

    E. Ryckman

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  1. E. Ryckman
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Ryckman, E. Linear Statistics of Point Processes via Orthogonal Polynomials. J Stat Phys 132, 473–486 (2008). https://doi.org/10.1007/s10955-008-9564-5

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  • DOI: https://doi.org/10.1007/s10955-008-9564-5

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