منابع مشابه
Approximating Orthogonal Matrices by Permutation Matrices
Motivated in part by a problem of combinatorial optimization and in part by analogies with quantum computations, we consider approximations of orthogonal matrices U by “non-commutative convex combinations”A of permutation matrices of the type A = P Aσσ, where σ are permutation matrices and Aσ are positive semidefinite n × n matrices summing up to the identity matrix. We prove that for every n× ...
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The main purpose of this paper is to look at the notion of partial transpose from the combinatorial side. In this perspective, we solve some basic enumeration problems involving partial transpose of permutation matrices. Specifically, we count the number of permutations matrices which are invariant under partial transpose. We count the number of permutation matrices which are still permutation ...
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The partial transpose of a block matrix M is the matrix obtained by transposing the blocks of M independently. We approach the notion of the partial transpose from a combinatorial point of view. In this perspective, we solve some basic enumeration problems concerning the partial transpose of permutation matrices. More specifically, we count the number of permutations matrices which are invarian...
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Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian but infinitely divisible. The fluctuations are asymptotically Gaussian for less smooth linear statistics for which the variance diverges. The degree of smooth...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1946
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500008610