On the maximal L1 influence of real-valued boolean functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916288808353792 |
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| author | Young, Andrew J. Pfister, Henry D. |
| author_facet | Young, Andrew J. Pfister, Henry D. |
| contents | 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 $Ω(\text{var}(f_n) \frac{\ln n}{n})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the maximal L1 influence of real-valued boolean functions Young, Andrew J. Pfister, Henry D. Discrete Mathematics 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 $Ω(\text{var}(f_n) \frac{\ln n}{n})$. |
| title | On the maximal L1 influence of real-valued boolean functions |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2406.10772 |