منابع مشابه
Tensor Products of Random Unitary Matrices
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. 2010 Mathematics Subject Classification. 15B52.
متن کاملTruncations of random unitary matrices
We analyse properties of non-Hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N > M , distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ...
متن کاملAddition of Free Unitary Random Matrices
We consider a new class of non–hermitian random matrices, namely the ones which have the form of sums of freely independent terms which involve unitary matrices. After deriving some general identities describing additive properties of unitary matrices, we solve three particular models: CUE plus CUE, CUE plus . . . plus CUE (i. e. the sum of an arbitrary number of CUE matrices), and CUE plus a r...
متن کاملSpectral Properties of Random Unitary Band Matrices
i It is a pleasure to thank Professor Stoiciu for his patience and selflessness in being my thesis advisor. Second, I would like to thank Professor Silva for being my second reader and for his helpful suggestions. Finally, I would like to thank my parents, without whom I could never have completed this thesis. One of the most important results in analysis is the Spectral Theorem, which shows th...
متن کاملAsymptotically Liberating Sequences of Random Unitary Matrices
A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asym...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random Matrices: Theory and Applications
سال: 2012
ISSN: 2010-3263,2010-3271
DOI: 10.1142/s2010326312500098