On a limiting point process related to modified permutation matrices
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In this article, the authors consider random permutation matrices following a one-parameter family of deformations of the uniform distribution, called Ewens' measures, and modifications of these matrices where the entries equal to one are replaced by i.i.d uniform random variables on the unit circle.Citations
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Maximum of the Characteristic Polynomial for a Random Permutation Matrix
TL;DR: In this paper, a logarithmic correlation structure for the maximum modulus of a uniform permutation matrix on the unit circle was shown to be a random field on the circle.
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Eigenvalue Fluctuations of Symmetric Group Permutation Representations on k-tuples and k-subsets
TL;DR: In this paper, it was shown that the normalized count of the number of eigenangles in a fixed interval of a permutation representation evaluated at a random element of the symmetric group σ ∈ \mathfrak{S}_n$ converges weakly to a compactly supported distribution.
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The Eigenvalue Point Process for Symmetric Group Permutation Representations on $k$-tuples
TL;DR: In this article, the eigenvalue point process of the permutation representation of the symmetric group (S) with the Ewens distribution was studied in the microscopic regime.
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On smooth mesoscopic linear statistics of the eigenvalues of random permutation matrices.
Valentin Bahier,Joseph Najnudel +1 more
TL;DR: In this article, the authors studied the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group.
References
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Logarithmic Combinatorial Structures: A Probabilistic Approach
TL;DR: In this article, the authors explain the similarities in asymptotic behaviour as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition.
Journal ArticleDOI
Eigenvalue distributions of random permutation matrices
TL;DR: For a fixed arc of the unit circle, the authors showed that the mean and variance of the eigenvalues of the permutation matrix are asymptotically distributed in the large $n$ limit.
Journal ArticleDOI
The distribution of eigenvalues of randomized permutation matrices
TL;DR: In this article, a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter � > 0) by replacing the entries equal to one by more general non- vanishing complex random variables is studied.
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Permutation Matrices, Wreath Products, and the Distribution of Eigenvalues
TL;DR: In this paper, the authors consider a class of random matrix ensembles which can be constructed from the random permutation matrices by replacing the nonzero entries of the n×n permutation matrix matrix with M×M diagonal matrices whose entries are random Kth roots of unity or random points on the unit circle.