- Statement
- See also
- References
- External links
In mathematics, the entropy influence conjecture is a statement about Boolean functions originally conjectured by Ehud Friedgut and Gil Kalai in 1996.[1]
Statement
For a function 
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).
See also
Analysis of Boolean functionsReferences
1. ^{{cite journal|last1=Friedgut|first1=Ehud|last2=Kalai|first2=Gil|title=Every monotone graph property has a sharp threshold|journal=Proceedings of the American Mathematical Society|volume=124|issue=10|year=1996|pages=2993–3002}}
- Unsolved Problems in Number Theory, Logic and Cryptography
- The Open Problems Project, discrete and computational geometry problems
External links
{{DEFAULTSORT:Entropy Influence Conjecture}} 2 : Entropy|Conjectures
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