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The distribution of eigenvalues of randomized permutation matrices

Joseph Najnudel, Ashkan Nikeghbali (2013)

Annales de l’institut Fourier

In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter θ > 0 ) by replacing the entries equal to one by more general non-vanishing complex random variables. For these ensembles, in contrast with more classical models as the Gaussian Unitary Ensemble, or the Circular Unitary Ensemble, the eigenvalues can be very explicitly computed by using the cycle structure of the permutations....

The fan graph is determined by its signless Laplacian spectrum

Muhuo Liu, Yuan Yuan, Kinkar Chandra Das (2020)

Czechoslovak Mathematical Journal

Given a graph G , if there is no nonisomorphic graph H such that G and H have the same signless Laplacian spectra, then we say that G is Q -DS. In this paper we show that every fan graph F n is Q -DS, where F n = K 1 P n - 1 and n 3 .

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