Probability Inequalities and Tail Estimates for Metric Semigroups
نویسنده
چکیده
We study probability inequalities leading to tail estimates in a general semigroup G with a translation-invariant metric dG . Using recent work [Ann. Prob., to appear] that extends the Hoffmann-Jørgensen inequality to all metric semigroups, we obtain tail estimates and approximate bounds for sums of independent semigroup-valued random variables, their moments, and decreasing rearrangements. In particular, we obtain the “correct” universal constants in several cases, extending results in the Banach space literature by Johnson–Schechtman–Zinn [Ann. Prob. 13], Hitczenko [Ann. Prob. 22], and Hitczenko and Montgomery-Smith [Ann. Prob. 29]. Our results also hold more generally, in the minimal mathematical framework required to state them: metric semigroups G . This includes all compact, discrete, or abelian Lie groups.
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