### Abstract

Let G be a locally compact unimodular group and μ an adapted spread out probability measure on G. We relate the rate of decay of the concentration functions associated with μ. to the growth of a certain subgroup N _{μ} of G. In particular, we show that when μ. is strictly aperiodic (i.e., when N_{μ}= G) and G satisfies the growth condition V_{G}(m) ≥ Cm^{D}, then for any compact neighborhood K ⊂ G we have sup_{g∈G} μ^{*n}(gK) ≤ C′n ^{-D/2}. This extends recent results of Retzlaff [R2] on discrete groups for adapted probability measures.

Original language | English (US) |
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Pages (from-to) | 1207-1222 |

Number of pages | 16 |

Journal | Illinois Journal of Mathematics |

Volume | 48 |

Issue number | 4 |

State | Published - Dec 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Illinois Journal of Mathematics*,

*48*(4), 1207-1222.

}

*Illinois Journal of Mathematics*, vol. 48, no. 4, pp. 1207-1222.

**Rate of decay of concentration functions for spread out measures.** / Cuny, Christophe; Retzlaff, Todd Matthew.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Rate of decay of concentration functions for spread out measures

AU - Cuny, Christophe

AU - Retzlaff, Todd Matthew

PY - 2004/12/1

Y1 - 2004/12/1

N2 - Let G be a locally compact unimodular group and μ an adapted spread out probability measure on G. We relate the rate of decay of the concentration functions associated with μ. to the growth of a certain subgroup N μ of G. In particular, we show that when μ. is strictly aperiodic (i.e., when Nμ= G) and G satisfies the growth condition VG(m) ≥ CmD, then for any compact neighborhood K ⊂ G we have supg∈G μ*n(gK) ≤ C′n -D/2. This extends recent results of Retzlaff [R2] on discrete groups for adapted probability measures.

AB - Let G be a locally compact unimodular group and μ an adapted spread out probability measure on G. We relate the rate of decay of the concentration functions associated with μ. to the growth of a certain subgroup N μ of G. In particular, we show that when μ. is strictly aperiodic (i.e., when Nμ= G) and G satisfies the growth condition VG(m) ≥ CmD, then for any compact neighborhood K ⊂ G we have supg∈G μ*n(gK) ≤ C′n -D/2. This extends recent results of Retzlaff [R2] on discrete groups for adapted probability measures.

UR - http://www.scopus.com/inward/record.url?scp=17244378058&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17244378058&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:17244378058

VL - 48

SP - 1207

EP - 1222

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

SN - 0019-2082

IS - 4

ER -