Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

Details Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

2006-03-03

arxiv.org/abs/math/0603098v1

Mathematics

Spectral Theory

27 pages

Scientific paper

We prove that for any $n\times n$ matrix, $A$, and $z$ with $|z|\geq \|A\|$,
we have that $\|(z-A)^{-1}\|\leq\cot (\frac{\pi}{4n}) \dist (z,
\spec(A))^{-1}$. We apply this result to the study of random orthogonal
polynomials on the unit circle.

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