Tensor Products of Random Unitary Matrices
Tomasz Tkocz, Marek Smaczynski, Marek Kus, Ofer Zeitouni, Karol, Zyczkowski
TL;DR
This paper studies the spectral properties of tensor products of random unitary matrices from the circular unitary ensemble, revealing conditions under which their spectral statistics become Poissonian.
Contribution
It demonstrates how the spectral statistics of tensor products of random unitary matrices transition to Poissonian under specific asymptotic regimes.
Findings
Spectral statistics become Poissonian when M=2 and N large.
Spectral statistics become Poissonian when N=2 and M large.
Spectral statistics become Poissonian when both M and N are large.
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.
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Taxonomy
TopicsRandom Matrices and Applications · Advanced Algebra and Geometry · Graph theory and applications