Point process convergence for the off-diagonal entries of sample covariance matrices

We study point process convergence for sequences of i.i.d. random walks. The objective is to derive asymptotic theory the extremes these show maximum walk Gumbel distribution under existence a (2+δ)th moment. make heavy use precise large deviation results sums variables. As consequence, we joint off-diagonal entries in sample covariance and correlation matrices high-dimensional whose dimension increases with size. This generalizes known on property largest entry.