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On the maximal L1 influence of real-valued boolean functions
Preprint
15 June 2024
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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 \(\Omega(\text{var}(f_n) \frac{\ln n}{n})\).