The Hoffmann–Jørgensen inequality in metric semigroups
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Apoorva Khare [1] ; Bala Rajaratnam [1]
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[1] Stanford University
Stanford University
Estados Unidos
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 1, 2017, págs. 4101-4111
- Idioma: inglés
- DOI: 10.1214/16-AOP1160
- Enlaces
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Resumen
We prove a refinement of the inequality by Hoffmann–Jørgensen that is significant for three reasons. First, our result improves on the state-of-the-art even for real-valued random variables. Second, the result unifies several versions in the Banach space literature, including those by Johnson and Schechtman [Ann. Probab. 17 (1989) 789–808], Klass and Nowicki [Ann. Probab. 28 (2000) 851–862], and Hitczenko and Montgomery-Smith [Ann. Probab. 29 (2001) 447–466]. Finally, we show that the Hoffmann–Jørgensen inequality (including our generalized version) holds not only in Banach spaces but more generally, in a very primitive mathematical framework required to state the inequality: a metric semigroup GG. This includes normed linear spaces as well as all compact, discrete or (connected) abelian Lie groups.
