Convenient Tail Bounds for Sums of Random Tensors

This work prepares new probability bounds for sums of random, independent, Hermitian tensors. These characterize large-deviation behavior the extreme eigenvalue random We extend Laplace transform method and Lieb's concavity theorem from matrices to tensors, apply these tools generalize classical associated with names Chernoff, Bennett, Bernstein scalar tensor setting. Tail norm a sum rectangular tensors are also derived corollaries cases. The proof mechanism can be applied tensor-valued martingales tensor-based Azuma, Hoeffding McDiarmid inequalities established.