•Instead of proving it –
assume it and let
•f : Rk ! [-1,1].
•N,M = standard normal vectors & E[Ni Mj] = h d(i = j).
•Define Sh(f) = E[f(N) f(M)].
•“Majority is Stablest” )
•Thm B: sup { Sh(f) : E[f] = 0} = 2 arcsin h / p.
•Pf: Approximate f by fn : {-1,1}k n ! {-1,1} with low influences and use Majority is
Stablest and the Central Limit Theorem.
•Thm B was proven by Borell 85.
•The optimizer f is the
• indicator of a half space.