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- W4287078275 abstract "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." @default.
- W4287078275 created "2022-07-25" @default.
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- W4287078275 date "2021-07-13" @default.
- W4287078275 modified "2023-09-30" @default.
- W4287078275 title "T product Tensors Part II: Tail Bounds for Sums of Random T product Tensors" @default.
- W4287078275 doi "https://doi.org/10.48550/arxiv.2107.06224" @default.
- W4287078275 hasPublicationYear "2021" @default.
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