•Conj (Khot-Kindler-M-O’Donnell-04)
•Thm(M-O’Donnell-Oleskiewicz-05):
•
•“Majority is Stablest”:
•
•For all h ¸ 0,
• limb ! 0 sup[Sh(f) : f: {-1,1}n ! [-1,1], I(f) · b, E[f] = 0]
• = (2 arcsin h)/ p
•
•Majn(x) := sgn(åi=1n xi) has
•I(Majn) ! 0 and Sh(Majn) ! (2 arcsin h)/p