Hölder-type inequalities and their applications to concentration and correlation bounds (1511.07204v1)

Abstract: Let $Y_v, v\in V,$ be $[0,1]$-valued random variables having a dependency graph $G=(V,E)$. We show that [ \mathbb{E}\left[\prod_{v\in V} Y_{v} \right] \leq \prod_{v\in V} \left{ \mathbb{E}\left[Y_v^{\frac{\chi_b}{b}}\right] \right}^{\frac{b}{\chi_b}}, ] where $\chi_b$ is the $b$-fold chromatic number of $G$. This inequality may be seen as a dependency-graph analogue of a generalised H\"older inequality, due to Helmut Finner. Additionally, we provide applications of H\"older-type inequalities to concentration and correlation bounds for sums of weakly dependent random variables.