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Correlation functions for random involutions

Forrester, Peter J. and Nagao, Taro and Rains, Eric M. (2006) Correlation functions for random involutions. International Mathematics Research Notices, 2006 . Art. No. 89796. ISSN 1073-7928. doi:10.1155/IMRN/2006/89796.

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Our interest is in the scaled joint distribution associated with k-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution for a Poissonized model in which both the number of symbols in the involution and the number of fixed points are random variables. From this, a de-Poissonization argument yields the scaled correlations and distribution function for the random involutions. These are found to coincide with the same quantities known in random matrix theory from the study of ensembles interpolating between the orthogonal and symplectic universality classes at the soft edge, the interpolation being due to a rank 1 perturbation.

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Additional Information:© 2006 Hindawi Publishing Corporation. Received: 31 August 2005; Revision Received: 15 March 2006; Accepted: 30 May 2006; Published: 01 January 2006. One of the authors (T.N.) is grateful to Dr. Tomohiro Sasamoto for valuable discussions. The referee is to be thanked for some useful suggestions. The work of PJF was supported by the Australian Research Council.
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Australian Research CouncilUNSPECIFIED
Record Number:CaltechAUTHORS:20171106-151415738
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Official Citation:Peter J. Forrester, Taro Nagao, Eric M. Rains; Correlation functions for random involutions, International Mathematics Research Notices, Volume 2006, 1 January 2006, 89796,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83003
Deposited By: Tony Diaz
Deposited On:06 Nov 2017 23:21
Last Modified:15 Nov 2021 19:54

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