Hölder-type inequalities and their applications to concentration and correlation bounds

Let Y v , v ∈ V , be real-valued random variables having a dependency graph G = (V, E). We show that E ⎡ ⎣ ∏ v∈V Y v ⎤ ⎦ ≤ ∏ v∈V { E [ Y χ b b v ]} b χ b , where χ b is the b-fold chromatic number of G. This inequality may be seen as a dependency-graph analogue of a generalised Hölder inequality, due to Helmut Finner. Additionally, we provide applications of the aforementioned Hölder-type inequalities to concentration and correlation bounds for sums of weakly dependent random variables whose dependencies can be described in terms of graphs or hypergraphs.

Jaar van publicatie:2016

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:1

CSS-citation score:1

Authors from:Higher Education

Toegankelijkheid:Open