The characteristic polynomial of a random permutation matrix. (English) Zbl 1047.60013
Summary: We establish a central limit theorem for the logarithm of the characteristic polynomial of a random permutation matrix. We relate this result to a central limit theorem of K. L. Wieand for the counting function for the eigenvalues lying in some interval on the unit circle.
MSC:
| 60F05 | Central limit and other weak theorems |
| 60G50 | Sums of independent random variables; random walks |
| 15B52 | Random matrices (algebraic aspects) |
References:
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