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Linear Statistics of Point Processes via Orthogonal Polynomials

Ryckman, E. (2008) Linear Statistics of Point Processes via Orthogonal Polynomials. Journal of Statistical Physics, 132 (3). pp. 473-486. ISSN 0022-4715. doi:10.1007/s10955-008-9564-5.

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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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Additional Information:© Springer Science+Business Media, LLC 2008. Received: 4 March 2008 / Accepted: 9 May 2008 / Published online: 28 May 2008. It is a pleasure to thank Rowan Killip for many helpful conversations during the preparation of this work, as well as the referee for relevant references to the literature.
Subject Keywords:Point processes; Random matrices; Orthogonal polynomials
Issue or Number:3
Record Number:CaltechAUTHORS:20180809-133558103
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Official Citation:Ryckman, E. J Stat Phys (2008) 132: 473.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88711
Deposited By: George Porter
Deposited On:09 Aug 2018 20:42
Last Modified:16 Nov 2021 00:29

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