Concentration Inequalities with Bounded Couplings

Stochastics Seminar
Thursday, April 3, 2014 - 15:05
1 hour (actually 50 minutes)
Skiles 005
University of Southern California
Let $Y$ be a nonnegative random variable with mean $\mu$, and let $Y^s$, defined on the same space as $Y$, have the $Y$ size biased distribution, that is, the distribution characterized by $\mathbb{E}[Yf(Y)]=\mu \mathbb{E}[f(Y^s)]$ for all functions $f$ for which these expectations exist. Under bounded coupling conditions, such as $Y^s-Y \leq C$ for some $C>0$, we show that $Y$ satisfies certain concentration inequalities around $\mu$. Examples will focus on occupancy models with log-concave marginal distributions.