In this talk, I will present a lecture given by Ramon Van Handel at the Saint-Flour summer school on non-asymptotic random matrix theory. I will present a very general result, that holds for any self-adjoint Gaussian matrix, that allows to control the expected operator norm of such a matrix. We will also be able to say things about the fluctuations of this quantity. The key ingredients will be the noncommutative Khintchine inequality and Gaussian concentration tools.
Note that it will be the first talk of a serie of 4 talks about the Pr. Van Handel's lecture.