Dissipation of Convolution Powers in a Metric Group

Wojciech Jaworski ()
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Wojciech Jaworski: Carleton University

Journal of Theoretical Probability, 2007, vol. 20, issue 3, 487-503

Abstract: Abstract In contrast to what is known about probability measures on locally compact groups, a metric group G can support a probability measure μ which is not carried on a compact subgroup but for which there exists a compact subset C⊆G such that the sequence μ n (C) fails to converge to zero as n tends to ∞. A noncompact metric group can also support a probability measure μ such that supp μ=G and the concentration functions of μ do not converge to zero. We derive a number of conditions which guarantee that the concentration functions in a metric group G converge to zero, and obtain a sufficient and necessary condition in order that a probability measure μ on G satisfy lim n→∞ μ n (C)=0 for every compact subset C⊆G.

Keywords: Convolution powers; Concentration functions; Metric groups; Random walks (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0072-3

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