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. https://resolver.caltech.edu/CaltechAUTHORS:20180809-133558103
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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.
Item Type: | Article | ||||||||||||
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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 | ||||||||||||
DOI: | 10.1007/s10955-008-9564-5 | ||||||||||||
Record Number: | CaltechAUTHORS:20180809-133558103 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180809-133558103 | ||||||||||||
Official Citation: | Ryckman, E. J Stat Phys (2008) 132: 473. https://doi.org/10.1007/s10955-008-9564-5 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 88711 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | George Porter | ||||||||||||
Deposited On: | 09 Aug 2018 20:42 | ||||||||||||
Last Modified: | 16 Nov 2021 00:29 |
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