{"title":"On the maximal L1 influence of real-valued boolean functions","authors":"Andrew J. Young, Henry D. Pfister","doi":"arxiv-2406.10772","DOIUrl":null,"url":null,"abstract":"We show that any sequence of well-behaved (e.g. bounded and non-constant)\nreal-valued functions of $n$ boolean variables $\\{f_n\\}$ admits a sequence of\ncoordinates whose $L^1$ influence under the $p$-biased distribution, for any\n$p\\in(0,1)$, is $\\Omega(\\text{var}(f_n) \\frac{\\ln n}{n})$.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"346 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.10772","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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 $\Omega(\text{var}(f_n) \frac{\ln n}{n})$.
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