## Abstract

We present new scalar and matrix Chernoff-style concentration bounds for a broad class of probability distributions over the binary hypercube {0, 1}n. Motivated by recent tools developed for the study of mixing times of Markov chains on discrete distributions, we say that a distribution is ℓ∞-independent when the infinity norm of its influence matrix is bounded by a constant. We show that any distribution which is ℓ∞-infinity independent satisfies a matrix Chernoff bound that matches the matrix Chernoff bound for independent random variables due to Tropp. Our matrix Chernoff bound is a broad generalization and strengthening of the matrix Chernoff bound of Kyng and Song (FOCS'18).

Original language | English |
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Title of host publication | ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 |

Publisher | Association for Computing Machinery |

Pages | 3732-3753 |

Number of pages | 22 |

ISBN (Electronic) | 9781611977073 |

State | Published - 2022 |

Event | 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 - Alexander, United States Duration: 9 Jan 2022 → 12 Jan 2022 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 2022-January |

### Conference

Conference | 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 |
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Country/Territory | United States |

City | Alexander |

Period | 9/01/22 → 12/01/22 |

### Bibliographical note

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