  In this article, we consider random Wigner matrices, that is symmetric
matrices such that the subdiagonal entries of Xn are independent, centered, and
with 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, the
law of the largest eigenvalue satisfies a large deviation principle with the
same rate function as in the Gaussian case. The crucial assumption is that the
Laplace transform of the entries must be bounded above by the Laplace transform
of a centered Gaussian variable with same variance. This is satisfied by the
Rademacher law and the uniform law on [sqrt{3}, sqrt{3}]. We extend our result
to complex entries Wigner matrices and Wishart matrices.
