Metric and Mixing Sufficient Conditions for Concentration of Measure

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dc.creatorKontorovich, Leonid
dc.date2006-10-13
dc.date2006-10-14
dc.date.accessioned2026-07-07T07:29:03Z
dc.date.available2026-07-07T07:29:03Z
dc.descriptionWe derive sufficient conditions for a family $(X^n,ρ_n,P_n)$ of metric probability spaces to have the measure concentration property. Specifically, if the sequence $\{P_n\}$ of probability measures satisfies a strong mixing condition (which we call $η$-mixing) and the sequence of metrics $\{ρ_n\}$ is what we call $Ψ$-dominated, we show that $(X^n,ρ_n,P_n)$ is a normal Levy family. We establish these properties for some metric probability spaces, including the possibly novel $X=[0,1]$, $ρ_n=\ell_1$ case.
dc.descriptionKeywords: concentration of measure, martingale differences, metric probability space, Levy family, strong mixing
dc.identifierhttps://arxiv.org/abs/math/0610427
dc.identifierhttp://arxiv.org/abs/math/0610427
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117956
dc.subjectProbability
dc.subjectFunctional Analysis
dc.subject60A99; 60G42
dc.titleMetric and Mixing Sufficient Conditions for Concentration of Measure
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