  This paper is the Part II of a serious work about T product tensors focusing
at establishing new probability bounds for sums of random, independent, T
product tensors. These probability bounds characterize large deviation behavior
of the extreme eigenvalue of the sums of random T product tensors. We apply
Lapalace transform method and Lieb concavity theorem for T product tensors
obtained from our Part I paper, and apply these tools to generalize the
classical bounds associated with the names Chernoff, and Bernstein from the
scalar to the T product tensor setting. Tail bounds for the norm of a sum of
random rectangular T product tensors are also derived from corollaries of
random Hermitian T product tensors cases. The proof mechanism is also applied
to T product tensor valued martingales and T product tensor based Azuma,
Hoeffding and McDiarmid inequalities are derived.
