Sharp Concentration of Simple Random Tensors

Abstract

This paper establishes sharp dimension-free concentration inequalities and expectation bounds for the deviation of the sum of simple random tensors from its expectation. As part of our analysis, we use generic chaining techniques to obtain a sharp high-probability upper bound on the suprema of $L_p$ empirical processes. In so doing, we generalize classical results for quadratic and product empirical processes to higher-order settings.