HOROWITZ SEMINAR
PROBABILITY, ERGODIC THEORY and DYNAMICAL SYSTEMS
On Monday January 9th in room 210, Schreiber Bldg., at
14:30
Sergey G. Bobkov (Minnesota)
Limit theorems and concentration inequalities for subsequences of random
variables.
abstract
It is well-known that any norm-bounded sequence of random variables
Xn in L2 contains a subsequence
Xnk which behave like shifted independent random
variables, possibly multiplied by an independent factor. In particular, if
Xn --> 0 weakly in L2, then
nk can be chosen such that
N-1/2 ( Xn1 + ... +
XnN ) ==> rZ
weakly in distribution, where Z is a standard normal random variable and
r is independent of Z. We will be discussing best rates of
increase of nk satisfying this form of the central limit
theorem.