10/28/2005
10
A proof sketch : new limit theorem
•
•
Recall:
p
a degree
k
multi-linear polynomial with:
•
|p|
2
= 1
and
I
i
(p)
·
d
for all
i
.
•
Want to show
p(x
1
,…,x
n
) ~ p(N
1
,…,N
n
).
•
Suffices to show that
8
smooth
F
(
|F’’’|
·
C
),
E[F(p(x
1
,…,x
n
)]
is close to
E[F(p(N
1
,…,N
n
))].
•
Proof similar to Lindberg proof of CLT
•
Uses Hypercontractivity