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Equidistribution of dilations of polynomial curves in nilmanifolds
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2009 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 137, no 6, 2111-2123 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the asymptotic behaviour under dilations of probability measures supported on polynomial curves in nilmanifolds. We prove, under some mild conditions, the effective equidistribution of such measures to the Haar measure. We also formulate a mean ergodic theorem for R-n-representations on Hilbert spaces, restricted to a moving phase of low dimension. Furthermore, we bound the necessary dilation of a given smooth curve in R-n so that the canonical projection onto T-n is epsilon-dense.

Place, publisher, year, edition, pages
2009. Vol. 137, no 6, 2111-2123 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-13947DOI: 10.1090/S0002-9939-09-09836-0ISI: 000263532900031Scopus ID: 2-s2.0-77951072821OAI: oai:DiVA.org:kth-13947DiVA: diva2:328532
Note
QC 20100705Available from: 2010-07-05 Created: 2010-07-05 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Limit Theorems for Ergodic Group Actions and Random Walks
Open this publication in new window or tab >>Limit Theorems for Ergodic Group Actions and Random Walks
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of an introduction, a summary and 7 papers. The papers are devoted to problems in ergodic theory, equidistribution on compact manifolds and random walks on groups.

In Papers A and B, we generalize two classical ergodic theorems for actions of abelian groups. The main result is a generalization of Kingman’s subadditive ergodic theorem to ergodic actions of the group Zd.

In Papers C,D and E, we consider equidistribution problems on nilmanifolds. In Paper C we study the asymptotic behavior of dilations of probability measures on nilmanifolds, supported on singular sets, and prove, under some technical assumptions, effective convergences to Haar measure. In Paper D, we give a new geometric proof of an old result by Koksma on almost sure equidistribution of expansive sequences. In paper E we give necessary and sufficient conditions on a probability measure on a homogeneous Riemannian manifold to be non–atomic.

Papers F and G are concerned with the asymptotic behavior of random walks on groups. In Paper F we consider homogeneous random walks on Gromov hyperbolic groups and establish a central limit theorem for random walks satisfying some technical moment conditions. Paper G is devoted to certain Bernoulli convolutions and the regularity of their value distributions.

Place, publisher, year, edition, pages
Stockholm: KTH, 2009. vii, 18 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 09:06
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-10451 (URN)
Public defence
2009-05-26, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 13:00 (English)
Opponent
Supervisors
Note
QC 20100705Available from: 2009-05-18 Created: 2009-05-15 Last updated: 2012-03-27Bibliographically approved

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