A Tail Bound for Read-k Families of Functions

Dmytro Gavinsky; Shachar Lovett; Michael Saks; Srikanth Srinivasan

A Tail Bound for Read-k Families of Functions

Discrete Mathematics 2022-03-30 v1 Probability

Authors: Dmytro Gavinsky , Shachar Lovett , Michael Saks , Srikanth Srinivasan

Abstract

We prove a Chernoff-like large deviation bound on the sum of non-independent random variables that have the following dependence structure. The variables $Y_1,...,Y_r$ are arbitrary Boolean functions of independent random variables $X_1,...,X_m$ , modulo a restriction that every $X_i$ influences at most $k$ of the variables $Y_1,...,Y_r$ .

Keywords

Chernoff bound tail bound read-k families Boolean functions limited dependence

Cite

@article{arxiv.1205.1478,
  title  = {A Tail Bound for Read-k Families of Functions},
  author = {Dmytro Gavinsky and Shachar Lovett and Michael Saks and Srikanth Srinivasan},
  journal= {arXiv preprint arXiv:1205.1478},
  year   = {2022}
}

A Tail Bound for Read-k Families of Functions

Abstract

Keywords

Cite

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