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We prove a large deviation principle for the largest eigenvalue of Wignermatrices without Gaussian tails, namely such that the distribution tails$\mathbb{P}( |X_{1,1}|>t)$ and $\mathbb{P}(|X_{1,2}|>t)$ behave like$e^{-bt^{\alpha}}$ and $e^{-at^{\alpha}}$ respectively for some $a,b\in(0,+\infty)$ and $\alpha\in (0,2)$. The large deviation principle is of speed$N^{\alpha/2}$ and with a good rate function depending only on the taildistribution of the entries.

Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails