Electronic Communications in Probability

A note on the tensor product of two random unitary matrices

Tomasz Tkocz

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Abstract

In this note we consider the point process of eigenvalues of the tensor product of two independent random unitary matrices of size m by m and n by n. When n becomes large, the process behaves like the superposition of m independent sine processes. When m and n go to infinity, we obtain the Poisson point process in the limit.

Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 16, 7 pp.

Dates
Accepted: 28 February 2013
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315555

Digital Object Identifier
doi:10.1214/ECP.v18-2484

Mathematical Reviews number (MathSciNet)
MR3037214

Zentralblatt MATH identifier
1308.60015

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
Secondary: 15B52: Random matrices

Keywords
Random matrices Circular Unitary Ensemble Tensor product Sine point process Poisson point process

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Tkocz, Tomasz. A note on the tensor product of two random unitary matrices. Electron. Commun. Probab. 18 (2013), paper no. 16, 7 pp. doi:10.1214/ECP.v18-2484. https://projecteuclid.org/euclid.ecp/1465315555


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References

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