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

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• 作者：Christos Pelekis ; ^{pelekis.chr@gmail.com} ; Jan Ramon ^{Jan.Ramon@cs.kuleuven.be} ; Yuyi Wang ^{yuyiwang920@gmail.com}
• 关键词：Fractional chromatic number ; Finner&rsquo ; s inequality ; Janson&rsquo ; s inequality ; Dependency graph ; Hypergraphs
• 刊名：Indagationes Mathematicae
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：28
• 期：1
• 页码：170-182
• 全文大小：288 K
• 卷排序：28

文摘

Let Yv,v∈VYv,v∈V, be real-valued random variables having a dependency graph G=(V,E)G=(V,E). We show that E∏v∈VYv≤∏v∈VEYvχbbbχb,where χbχb is the bb-fold chromatic number of GG. 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.