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- W1488396002 abstract "Let $H_{0}$ be an arbitrary self-adjoint $ntimes n$ matrix and $H(n)$ be an $ntimes n$ (random) Wigner matrix. We show that $tmapsto operatorname {Tr} exp (H(n)-mathrm {i} tH_{0})$ is positive definite in the average. This partially answers a long-standing conjecture. On the basis of asymptotic freeness our result implies that $tmapsto tau (exp (a- text {i} tb))$ is positive definite whenever the noncommutative random variables $a$ and $b$ are in free relation, with $a$ semicircular." @default.
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- W1488396002 date "2003-02-20" @default.
- W1488396002 modified "2023-09-27" @default.
- W1488396002 title "Perturbation of Wigner matrices and a conjecture" @default.
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- W1488396002 doi "https://doi.org/10.1090/s0002-9939-03-06813-8" @default.
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