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We establish large deviations estimates for the largest eigenvalue of Wigner matrices with sub-Gaussian entries. We estimate the probability that the largest eigenvalue is close to some value large enough and show that if the entries do not have sharp sub-Gaussian tails, the rate function is strictly smaller than the rate function for Gaussian entries. This contrasts with [12] where it was shown that the law of the largest eigenvalue of Wigner matrices with entries with sharp sub-Gaussian tails obeys a large deviation principle with the same rate function than in the Gaussian case.

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