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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
##### Keywords:
random matrices; large deviations
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