A new limit theorem [M+ODonnell+Oleszkiewicz(05)]:
Let f : {-1,1}n ! R be a degree k multi-linear polynomial,
f(x)
= ε0 < |S| · k aS Υi 2 S xi such that
|f|2 = 1
I (f) · d.
Then for all t:
|P[f · t] - P[ε0 < |S| · k aS Υi 2 S Ni · t]| · O(k d1/(4k))
We prove similar result for other discrete spaces.
Generalizes:
CLT
Gaussian chaos results for U and V statistics.