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

Abstract : 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.
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Submitted on : Wednesday, January 11, 2017 - 11:07:27 PM
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Christos Pelekis, Jan Ramon, Yuyi Wang. Hölder-type inequalities and their applications to concentration and correlation bounds. Indagationes Mathematicae, Elsevier, 2017, 28 (1), pp.170-182. ⟨10.1016/j.indag.2016.11.017⟩. ⟨hal-01421953⟩

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