This question is related to my earlier question here .

Given an $n\times n$ random matrix $A$, is determining the properties (mean, variance,moments,etc.) of its induced $p$-norm ($p\neq 0,1,2,\infty$) a good research problem?

Looking at related work, I couldn't find anything much except a paper by Hansen on the 2-norm here . Also Terence Tao's page here on random matrices talks about singular values of a random matrix ; I don't know if there is a trivial extension from these results to determining its $p$ -norm.

I don't have a pure maths background and would much appreciate suggestions.