TENSOR PRODUCTS OF RANDOM UNITARY MATRICES
Abstract
Tensor products of M random unitary matrices of size N from the circular unitary ensemble are investigated. We show that the spectral statistics of the tensor product of random matrices becomes Poissonian if M = 2, N become large or M become large and N = 2.
References
-
G. Anderson , A. Guionnet and O. Zeitouni , An Introduction to Random Matrices ,Cambridge Studies in Advanced Mathematics 118 ( Cambridge University Press , Cambridge , 2010 ) . Google Scholar -
R. N. Bhattacharya and R. Ranga Rao , Normal Approximation and Asymptotic Expansions ,Classics in Applied Mathematics 64 ( SIAM , Philadelphia , 2010 ) . Crossref, Google Scholar - J. Math. Phys. 3, 140 (1962), DOI: 10.1063/1.1703773. Crossref, Google Scholar
P. J. Forrester and E. M. Rains , Random Matrix Models and their Applications,Mathematical Sciences Research Institute Publications 40 (Cambridge University Press, Cambridge, 2001) pp. 171–207. Google Scholar-
R. L. Graham , D. E. Knuth and O. Patashnik , Concrete Mathematics ( Addison-Wesley , 1998 ) . Google Scholar - Commun. Math. Phys. 265, 95 (2006), DOI: 10.1007/s00220-006-1535-6. Crossref, Google Scholar
-
Z. Lin and Z. Bai , Probability Inequalities ( Springer , Heidelberg , 2010 ) . Google Scholar -
M. L. Mehta , Random Matrices , 3rd edn. ( Elsevier/Academic Press , Amsterdam , 2004 ) . Google Scholar - Phys. Rev. 120, 1698 (1960), DOI: 10.1103/PhysRev.120.1698. Crossref, Google Scholar
- J. Phys. A 34, 7111 (2001). Crossref, Google Scholar