Entropy influence conjecture

In mathematics, the entropy influence conjecture is a statement about Boolean functions originally conjectured by Ehud Friedgut and Gil Kalai in 1996.

note its Fourier expansion The entropy–influence conjecture states that there exists an absolute constant C such that

where the total influence

is defined by and the entropy

(of the spectrum) is defined by (where x log x is taken to be 0 when x = 0).