Contractive Automorphisms of Locally Compact Groups and the Concentration Function Problem

Wojciech Jaworski ()

Journal of Theoretical Probability, 1997, vol. 10, issue 4, 967-989

Abstract: Abstract Let G be a noncompact locally compact group. We show that a necessary and sufficient condition in order that G support an adapted probability measure whose concentration functions fail converge to zero is that G be the semidirect product $$N \times _\tau \mathbb{Z}$$ , where τ is an automorphism of N contractive modulo a compact subgroup. Any adapted a probability measure whose concentration functions fail to converge to zero has the form μ=v×δ1 where v is a probability measure on N. If G is unimodular then the concentration functions of an adapted probability measure μ fail to converge to zero if and only if μ is supported on a coset of a compact normal subgroup.

Keywords: Concentration functions; locally compact groups; contractive automorphisms; random walks (search for similar items in EconPapers)
Date: 1997
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1023/A:1022666717516 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:10:y:1997:i:4:d:10.1023_a:1022666717516

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1022666717516

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().