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

Tijdschriftbijdrage - Tijdschriftartikel

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.
Tijdschrift: Indagationes Mathematicae
ISSN: 0019-3577
Issue: 1
Volume: 28
Pagina's: 170 - 182
Jaar van publicatie:2016