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Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails. (English) Zbl 1338.60010
Summary: 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 \(\mathbb{P} ( |X_{1,1}|>t)\) and off-diagonal entries \(\mathbb{P} (|X_{1,2}|>t)\) behave like \(e^{-bt^{\alpha }}\) and \(e^{-at^{\alpha }}\) respectively, for some \(a,b\in (0,+\infty )\) and \(\alpha \in (0,2)\). The large deviations principle is of speed \(N^{\alpha /2}\), and with a good rate function depending only on the distribution tail of the entries.
Reviewer: Reviewer (Berlin)

MSC:
60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
60F10 Large deviations
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