Logarithmic law of large random correlation matrices

Nestor Parolya, Johannes Heiny, Dorota Kurowicka

Consider a random vector $\mathbf{y}={\mathbf{\Sigma }}^{1/2}\mathbf{x}$, where the $p$ elements of the vector $\mathbf{x}$ are i.i.d. real-valued random variables with zero mean and finite…