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• W2950733268 abstract "Let $X_N$ be an $Nts N$ random symmetric matrix with independent equidistributed entries. If the law $P$ of the entries has a finite second moment, it was shown by Wigner cite{wigner} that the empirical distribution of the eigenvalues of $X_N$, once renormalized by $sqrt{N}$, converges almost surely and in expectation to the so-called semicircular distribution as $N$ goes to infinity. In this paper we study the same question when $P$ is in the domain of attraction of an $alpha$-stable law. We prove that if we renormalize the eigenvalues by a constant $a_N$ of order $N^{frac{1}{alpha}}$, the corresponding spectral distribution converges in expectation towards a law $mu_alpha$ which only depends on $alpha$. We characterize $mu_alpha$ and study some of its properties; it is a heavy-tailed probability measure which is absolutely continuous with respect to Lebesgue measure except possibly on a compact set of capacity zero." @default.
• W2950733268 created "2019-06-27" @default.
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• W2950733268 date "2007-07-14" @default.
• W2950733268 modified "2023-10-01" @default.
• W2950733268 title "The spectrum of heavy-tailed random matrices" @default.
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