On the norm of Gaussian random matrices

Pierre Youssef
Université de Paris VII (Denis Diderot)

We consider a symmetric random matrix whose entries on and above the diagonal are independent Gaussian random variables with any variance pattern. We study the operator norm of this matrix and show that its distribution is comparable to that of the maximum Euclidean norm of the rows of the matrix, settling a conjecture of Latala. The expectation of the norm has an explicit formula in terms of the variance pattern and our result extends to more general Schatten norms. This is a joint work with Ramon Van Handel and Rafal Latala.

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