Wenbo V. Li
Title: Gaussian Inequalities and Conjectures
Abstract: Given $d$ real valued random variables $X_1, \cdots, X_d$,
there are various ways to measure dependence structures among them, such as correlations,
mixed moments, etc.
In this talk, we define and study a new measure that captures the amount of dependence
when it is compared with the ``best'' independent ones. To be more precise, we consider the
best (largest constant $\alpha$ and smallest constant $\beta$) possible probability bounds
$$
\alpha \prod_{i=1}^d \P(W_i\in B_i)
\le \P( \cap_{i=1}^d \{X_i \in B_i\} ) \le \beta \prod_{i=1}^d \P(Y_i\in B_i)
$$
for some real valued random variables $W_i$, $Y_i$,
and all Borel sets $B_i$, $1 \le i \le d$.
The joint Gaussian case is studied in detail.
Corrections:
Updated relevant references:
Last modified Oct. 10, 2010 by Wenbo V. Li,
wli@math.udel.edu