Applications of Bounded Size Bias Couplings for Concentration of Measure
Probability Seminar
Apr 13, 2011, 03:10 PM - 04:00 PM | 332 Evans Hall | Happening As Scheduled
Larry Goldstein, Department of Mathematics, University of Southern California
For a nonnegative random variable Y with finite nonzero mean µ, we say that Y^s has the
Y-size bias distribution if
E[Y f (Y)] = µEf [(Y^s)] for all smooth f .
If a bounded size biased coupling for Y exists, that is, if Y can be coupled to Y^s
having the Y -size bias distribution such that for some constant C we have
|Y^s − Y | ≤ C
almost surely, then Y satisfies...