Abstract
We prove a large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails, that is, the distribution tails of the diagonal entries P(|X1,1|>t) and off-diagonal entries P(|X1,2|>t) behave like e−btα and e−atα respectively, for some a,b∈(0,+∞) and α∈(0,2). The large deviations principle is of speed Nα/2, and with a good rate function depending only on the distribution tail of the entries.
Citation
Fanny Augeri. "Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails." Electron. J. Probab. 21 1 - 49, 2016. https://doi.org/10.1214/16-EJP4146
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