•Idea: Truncate and follow your
nose.
•Suppose f : {-1,1}n ! [-1,1] has small influences but E[f Tr f] = is large.
•Then the same is true for g = Tq f (q(r) < 1).
•Let h = å|S| · k gS uS then |h-g|2 is small.
•Let h’ = å|S| · k gS Õi 2 S Ni
•Then: <h,Tr h> = <h’, Ur h’> is large and by the new limit theorem:
•h’ is close in L2 to a [-1,1] R.V.
•Take g’(x) = h’(x) if |h’(x)| · 1
and g’(x)
= sgn(h’(x)).
•E[g’ Ur g’] is too large – contradiction!
•