Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Almost sure equidistribution in expansive families
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2009 (English)In: Indagationes mathematicae, ISSN 0019-3577, Vol. 20, no 2, 167-177 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study generic equidistribution in families of sequences of points on tori. We assume that the sequences are parameterized by some subset of a Euclidean space, and we formulate geometric conditions on the dependence so that equidistribution holds almost everywhere with respect to the Lebesgue measure on the parameter space. As a consequence, we can give a new proof of an old result by Koksma.

Place, publisher, year, edition, pages
2009. Vol. 20, no 2, 167-177 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-13948DOI: 10.1016/S0019-3577(09)00017-2ISI: 000274561400001Scopus ID: 2-s2.0-77449137486OAI: oai:DiVA.org:kth-13948DiVA: diva2:328533
Note
QC 20100705Available from: 2010-07-05 Created: 2010-07-05 Last updated: 2010-08-09Bibliographically 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
2. Viana maps and limit distributions of sums of point measures
Open this publication in new window or tab >>Viana maps and limit distributions of sums of point measures
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: US-AB, 2009. vii, 37 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 09:14
Keyword
Viana maps, absolutely continuous invariant measures, skew-products, quadratic maps, Bernoulli convolutions, absolute continuity, typical points, equidistributed sequences, uniformly distibuted sequences
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-11477 (URN)978-91-7415-521-1 (ISBN)
Public defence
2009-12-17, Kollegiesalen F3, Kungl Tekniska högskolan, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2009-12-03 Created: 2009-11-16 Last updated: 2012-02-24Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Björklund, MichaelSchnellmann, Daniel
By organisation
Mathematics (Dept.)
In the same journal
Indagationes mathematicae
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 40 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf