2021/07/13 by Shih Yu Chang, Yimin Wei, Chang, Shih Yu +1
Chemistry · Mathematics · #Advanced NMR Techniques and Applications #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2107.06224
openalex publication_date 2021/07/13 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.