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On smooth mesoscopic linear statistics of the eigenvalues of random permutation matrices
Valentin Bahier, Joseph Najnudel
We study 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 me…
On a limiting point process related to modified permutation matrices
Valentin Bahier
We consider random permutation matrices following a one-parameter family of deformations of the uniform distribution, called Ewens' measures, and modifications of these matrices wh…
Characteristic polynomials of modified permutation matrices at microscopic scale
Valentin Bahier
We study the characteristic polynomial of random permutation matrices following some measures which are invariant by conjugation, including Ewens' measures which are one-parameter…
On the number of eigenvalues of modified permutation matrices in mesoscopic intervals
Valentin Bahier
We are interested in two random matrix ensembles related to permutations: the ensemble of permutation matrices following Ewens' distribution of a given parameter , and its mod…