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

2015/11/23 by Christos Pelekis, Jan Ramon, Pelekis, Christos +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1511.07204

15 pages

arxiv created 2015/11/23 · arxiv updated 2015/11/24

Abstract

Let Y_v, v∈ V, be [0,1]-valued random variables having a dependency graph G=(V,E). We show that 𝔼[∏_{v∈ V} Y_v ] ≤ ∏_{v∈ V} \ 𝔼[Y_v^(χ_b)/(b)] \^(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 Hölder-type inequalities to concentration and correlation bounds for sums of weakly dependent random variables.

Related

• Hoeffding's inequality for sums of weakly dependent random variables
• Conditioned Poisson distributions and the concentration of chromatic numbers
• Concentration Inequalities for Incomplete U-statistics over Arbitrary Sampling Graphs
• Concentration inequalities with exchangeable pairs (Ph.D. thesis)
• Concentration inequality using unconfirmed knowledge