This question is related to my earlier question 
[here](http://tiny.cc/ga9k1) .


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](http://portal.acm.org/citation.cfm?id=49940) . Also Terence Tao's page  [here](http://terrytao.wordpress.com/2009/08/15/random-matrices-universality-of-local-eigenvalue-statistics-up-to-the-edge/)  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.



Induced p-norm of a Random matrix
Here are some papers you might want to look at if you're interested in this issue (probably better than the paper of mine that Suvrit mentioned):


1. [G. Bennett, V. Goodman, and C.M. Newman. Norms of random matrices.
Pacific J. Math. 59 (1975), no. 2, 359–365.](http://projecteuclid.org/euclid.pjm/1102905342)
2. Grahame Bennett. Lectures on matrix transformations of $l\_p$ spaces. Notes in Banach spaces, pp. 39--80, Univ. Texas Press, Austin, Tex., 1980. (specifically, section 4 of this paper)
3. Stanisław Szarek. Condition numbers of random matrices. J. Complexity 7 (1991), no. 2, 131–149.
4. [Kenneth R. Davidson and Stanislaw J. Szarek. Local operator theory, random matrices and Banach spaces. Handbook of the geometry of Banach spaces, Vol. I, 317–366, North-Holland, Amsterdam, 2001.](http://www.cwru.edu/artsci/math/szarek/TeX/DavSzaHB.pdf) (specifically, the end of section 2.3 of this paper)


The third of these deals explicitly with the question of deducing results about the induced $p$-norm from results about singular values.


