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In this article, we consider random Wigner matrices, that is symmetricmatrices such that the subdiagonal entries of Xn are independent, centered, andwith variance one except on the diagonal where the entries have variance two.We prove that, under some suitable hypotheses on the laws of the entries, thelaw of the largest eigenvalue satisfies a large deviation principle with thesame rate function as in the Gaussian case. The crucial assumption is that theLaplace transform of the entries must be bounded above by the Laplace transformof a centered Gaussian variable with same variance. This is satisfied by theRademacher law and the uniform law on [sqrt{3}, sqrt{3}]. We extend our resultto complex entries Wigner matrices and Wishart matrices.

Large deviations for the largest eigenvalue of Rademacher matrices