A note on the tensor product of two random unitary matrices

Tomasz Tkocz (University of Warwick)

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.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 1-7

Publication Date: February 28, 2013

DOI: 10.1214/ECP.v18-2484

References

  • Anderson, Greg W.; Guionnet, Alice; Zeitouni, Ofer. An introduction to random matrices. Cambridge Studies in Advanced Mathematics, 118. Cambridge University Press, Cambridge, 2010. xiv+492 pp. ISBN: 978-0-521-19452-5 MR2760897
  • Breuer, Heinz-Peter; Petruccione, Francesco. The theory of open quantum systems. Oxford University Press, New York, 2002. xxii+625 pp. ISBN: 0-19-852063-8 MR2012610
  • Camilier, I.; Decreusefond, L. Quasi-invariance and integration by parts for determinantal and permanental processes. J. Funct. Anal. 259 (2010), no. 1, 268--300. MR2610387
  • Hough, J. Ben; Krishnapur, Manjunath; Peres, Yuval; Virág, Bálint. Zeros of Gaussian analytic functions and determinantal point processes. University Lecture Series, 51. American Mathematical Society, Providence, RI, 2009. x+154 pp. ISBN: 978-0-8218-4373-4 MR2552864
  • T. Tkocz, M. Smaczyński, M. Kuś, O. Zeitouni, K. Życzkowski, Tensor Products of Random Unitary Matrices, phRandom Matrices: Theory and Applications, Vol. 1, No. 4 (2012) 1250009 (26 pages).


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