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Improved bounds on Fourier entropy and Min-entropy
[article]

2021
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arXiv
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pre-print

Given a Boolean function f:{-1,1}^n→{-1,1}, the Fourier distribution assigns probability f(S)^2 to S⊆ [n]. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai asks if there exist a universal constant C>0 such that H(f̂^2)≤ C Inf(f), where H(f̂^2) is the Shannon entropy of the Fourier distribution of f and Inf(f) is the total influence of f. 1) We consider the weaker Fourier Min-entropy-Influence (FMEI) conjecture. This asks if H_∞(f̂^2)≤ C Inf(f), where H_∞(f̂^2) is the

arXiv:1809.09819v2
fatcat:xdvzfqhxzbfubndtq3hudfrkey