2021
DOI: 10.48550/arxiv.2111.02177
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Scalar and Matrix Chernoff Bounds from $\ell_{\infty}$-Independence

Abstract: We show new scalar and matrix Chernoff-style concentration bounds for a broad class of probability distributions over {0, 1} n . Building on developments in high-dimensional expanders (Kaufman and Mass ITCS'17, Dinur and Kaufman FOCS'17, Kaufman and Oppenheim Combinatorica'20) and matroid theory (Adiprasito et al. Ann. Math.'18), a breakthrough result of Anari, Liu, Oveis and Vinzant (STOC '19) showed that the up-down random walk on matroid bases has polynomial mixing time -making it possible to efficiently … Show more

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