Geodesic
On concentrated probabilities
Annales Polonici Mathematici, Tome 61 (1995) no. 1, pp. 25-38.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence $g_n ∈ G$ such that $μ^{∗n}(g_n A) ≡ 1$ for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power $μ^{∗k}$ has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological group G.
DOI : 10.4064/ap-61-1-25-38
Keywords: random walk, concentration function, convolution operator

Wojciech Bartoszek 1

1 
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Wojciech Bartoszek. On concentrated probabilities. Annales Polonici Mathematici, Tome 61 (1995) no. 1, pp. 25-38. doi : 10.4064/ap-61-1-25-38. http://geodesic.mathdoc.fr/articles/10.4064/ap-61-1-25-38/

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