The subgaussian constant and concentration inequalities
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We study concentration inequalities for Lipschitz functions on graphs by estimating the optimal constant in exponential moments of subgaussian type. This is illustrated on various graphs and related to various graph constants. We also settle, in the affirmative, a question of Talagrand on a deviation inequality for the discrete cube.
KeywordsLipschitz Function Isoperimetric Inequality Logarithmic Sobolev Inequality Isoperimetric Problem Expander Graph
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