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- W2034384973 abstract "Let $W = (X_{ij}; 1 leq i, j < infty)$ be an infinite matrix. Suppose $W$ is symmetric, entries on the diagonal are $operatorname{iid}$, entries off the diagonal are $operatorname{iid}$ and they are independent. Then it is proved that the necessary and sufficient conditions for $lambda_{max}((1/sqrt{n})W_n) rightarrow a mathrm{a.s.}$ are (1) $E(X^+_{11})^2 < infty$; (2) $EX^4_{12} < infty$; (3) $EX_{12} leq 0$; (4) $a = 2sigma, sigma^2 = EX^2_{12}$. Here $W_n = (X_{ij}; 1 leq i, j leq n)$." @default.
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- W2034384973 date "1988-10-01" @default.
- W2034384973 modified "2023-09-29" @default.
- W2034384973 title "Necessary and Sufficient Conditions for Almost Sure Convergence of the Largest Eigenvalue of a Wigner Matrix" @default.
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- W2034384973 doi "https://doi.org/10.1214/aop/1176991594" @default.
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