English

On the maximal L1 influence of real-valued boolean functions

Discrete Mathematics 2024-06-18 v1

Abstract

We show that any sequence of well-behaved (e.g. bounded and non-constant) real-valued functions of nn boolean variables {fn}\{f_n\} admits a sequence of coordinates whose L1L^1 influence under the pp-biased distribution, for any p(0,1)p\in(0,1), is Ω(var(fn)lnnn)\Omega(\text{var}(f_n) \frac{\ln n}{n}).

Keywords

Cite

@article{arxiv.2406.10772,
  title  = {On the maximal L1 influence of real-valued boolean functions},
  author = {Andrew J. Young and Henry D. Pfister},
  journal= {arXiv preprint arXiv:2406.10772},
  year   = {2024}
}
R2 v1 2026-06-28T17:07:28.108Z