Sums of Random Symmetric Matrices and Applications

Let B_i be deterministic symmetric m\times m matrices, and \xi_i be independent random scalars with zero mean and “of order of one” (e.g., \xi_i are Gaussian with zero mean and unit standard deviation). We are interested in conditions for the “typical norm” of the random matrix S_N = \xi_1B_1+…+\xi_NB_N to be of order of 1. … Read more