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Thinning and conditioning of the circular unitary ensemble

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Charlier, Christophe [UCL] Claeys, Tom [UCL]

We apply the operation of random independent thinning on the eigenvalues of n×n Haar distributed unitary random matrices. We study gap probabilities for the thinned eigenvalues, and we study the statistics of the eigenvalues of random unitary matrices which are conditioned such that there are no thinned eigenvalues on a given arc of the unit circle. Various probabilistic quantities can be expressed in terms of Toeplitz determinants and orthogonal polynomials on the unit circle, and we use these expressions to obtain asymptotics as n→∞.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2017
Language Anglais
Journal information "Random Matrices: Theory and Applications" - Vol. 6, p. 51 pages (2017)
Peer reviewed yes
Publisher World Scientific Publishing Co. Pte. Ltd. (Singapore)
issn 2010-3263
e-issn 2010-3271
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
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Bibliographic reference Charlier, Christophe ; Claeys, Tom. Thinning and conditioning of the circular unitary ensemble. In: Random Matrices: Theory and Applications, Vol. 6, p. 51 pages (2017)
Permanent URL http://hdl.handle.net/2078.1/190609