Lovett, S.,Moore, C.,Russell, A.
We show that there exists a family of groups G(n) and nontrivial irreducible representations (n) such that, for any constant t, the average of rho(n) over t uniformly random elements g(1), ... , g(t) is an element of G(n) has operator norm 1 with probability approaching 1 as n --> infinity. More quantitatively, we show that there exist families of finite groups for which Omega (log log vertical bar G vertical bar) random elements are required to bound the norm of a typical representation below 1. This settles a conjecture of A. Wigderson.