On the maximal L1 influence of real-valued boolean functions
<|reference_start|>On the maximal L1 influence of real-valued boolean functions: We show that any sequence of well-behaved (e.g. bounded and non-constant) real-valued functions of $n$ boolean variables $\{f_n\}$ admits a sequence of coordinates whose $L^1$ influence under the $p$-biased distribution, for any $p\in(0,1)$, is $\Omega(\text{var}(f_n) \frac{\ln n}{n})$.<|reference_end|>
@article{young2024on,
    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},
    archivePrefix={arXiv},
    eprint={2406.10772},
    primaryClass={cs.DM}
}