10/28/2005

10

•__Recall:__ p a degree k multi-linear polynomial
with:

•|p|2 = 1 and Ii(p) · d for all i.

•Want to show p(x1,…,xn) ~ p(N1,…,Nn).

•Suffices to show that 8 smooth F ( |F’’’| · C ), E[F(p(x1,…,xn)] is close to E[F(p(N1,…,Nn))].

• Proof similar to
Lindberg proof of CLT

• Uses Hypercontractivity