Published August 2008
| Accepted Version
Journal Article
Open
Linear Statistics of Point Processes via Orthogonal Polynomials
- Creators
- Ryckman, E.
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.
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.Attached Files
Accepted Version - 0805.3516
Files
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Additional details
- Eprint ID
- 88711
- DOI
- 10.1007/s10955-008-9564-5
- Resolver ID
- CaltechAUTHORS:20180809-133558103
- Created
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2018-08-09Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field