On concentrated probabilities on non locally compact groups

Wojciech Bartoszek

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 3, page 635-640
  • ISSN: 0010-2628

Abstract

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Let G be a Polish group with an invariant metric. We characterize those probability measures μ on G so that there exist a sequence g n G and a compact set A G with   μ * n ( g n A ) 1   for all n .

How to cite

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Bartoszek, Wojciech. "On concentrated probabilities on non locally compact groups." Commentationes Mathematicae Universitatis Carolinae 37.3 (1996): 635-640. <http://eudml.org/doc/247932>.

@article{Bartoszek1996,
abstract = {Let $G$ be a Polish group with an invariant metric. We characterize those probability measures $\mu $ on $G$ so that there exist a sequence $g_n \in G$ and a compact set $A \subseteq G$ with   $\{\mu \}^\{*n\} (g_n A) \equiv 1$   for all $n$.},
author = {Bartoszek, Wojciech},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {concentration function; random walk; Markov operator; invariant measure; concentrated probability; random walk; Markov operator; Polish group; invariant metric},
language = {eng},
number = {3},
pages = {635-640},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On concentrated probabilities on non locally compact groups},
url = {http://eudml.org/doc/247932},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Bartoszek, Wojciech
TI - On concentrated probabilities on non locally compact groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 3
SP - 635
EP - 640
AB - Let $G$ be a Polish group with an invariant metric. We characterize those probability measures $\mu $ on $G$ so that there exist a sequence $g_n \in G$ and a compact set $A \subseteq G$ with   ${\mu }^{*n} (g_n A) \equiv 1$   for all $n$.
LA - eng
KW - concentration function; random walk; Markov operator; invariant measure; concentrated probability; random walk; Markov operator; Polish group; invariant metric
UR - http://eudml.org/doc/247932
ER -

References

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  1. Bartoszek W., On concentrated probabilities, Ann. Polon. Math. 61.1 (1995), 25-38. (1995) Zbl0856.22006MR1318315
  2. Bartoszek W., The structure of random walks on semidirect products, Bull. L'Acad. Pol. Sci. ser. Sci. Math. Astr. & Phys. 43.4 (1995), 277-282. (1995) Zbl0849.22006MR1414784
  3. Csiszár I., On infinite products of random elements and infinite convolutions of probability distributions on locally compact groups, Z. Wahrsch. Verw. Gebiete 5 (1966), 279-299. (1966) MR0205306
  4. Jaworski W., Rosenblatt J., Willis G., Concentration functions in locally compact groups, preprint, 17 pages, 1995. Zbl0854.43001MR1399711
  5. Parthasarathy K.R., Introduction to Probability and Measure, New Delhi, 1980. Zbl1075.28001
  6. Sine R., Geometric theory of a single Markov operator, Pacif. J. Math. 27.1 (1968), 155-166. (1968) Zbl0281.60083MR0240281

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