10/28/2005

9

•__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!__

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