Eigenvalue distributions of random permutation matrices
Wieand, Kelly
Ann. Probab., Tome 28 (2000) no. 1, p. 1563-1587 / Harvested from Project Euclid
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Let $M$ be a randomly chosen $n \times n$ permutation matrix. For a fixed arc of the unit circle, let $X$ be the number of eigenvalues of $M$ which lie in the specified arc. We calculate the large $n$ asymptotics for the mean and variance of $X$, and show that $(X -E[X])/( \Var (X))^ 1/2$ is asymptotically normally distributed. In addition, we show that for several fixed arcs $I_1,\ldots,I_m$, the corresponding random variables are jointly normal in the large $n$ limit.
Publié le : 2000-10-14
Classification:  Permutations,  random matrices,  15A52,  60B15,  60F05,  60C05 
@article{1019160498,
     author = {Wieand, Kelly},
     title = {Eigenvalue distributions of random permutation matrices},
     journal = {Ann. Probab.},
     volume = {28},
     number = {1},
     year = {2000},
     pages = { 1563-1587},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1019160498}
}

Wieand, Kelly. Eigenvalue distributions of random permutation matrices. Ann. Probab., Tome 28 (2000) no. 1, pp.  1563-1587. http://gdmltest.u-ga.fr/item/1019160498/