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Almost sure absolute continuity of Bernoulli convolutions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). (Analysgruppen)
2010 (English)In: Ann. Inst. H. Poincaré Probab. Statist., ISSN 0246-0203, Vol. 46, no 3, 888-893 p.Article in journal (Refereed) Published
Abstract [en]

We prove an extension of a result by Peres and Solomyak on almostsure absolute continuity in a class of symmetric Bernoulli convolutions.

Place, publisher, year, edition, pages
2010. Vol. 46, no 3, 888-893 p.
Keyword [en]
Bernoulli convolutions; Absolute continuity
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-11647DOI: 10.1214/09-AIHP334ISI: 000283528100013Scopus ID: 2-s2.0-77955640920OAI: oai:DiVA.org:kth-11647DiVA: diva2:278692
Funder
Knut and Alice Wallenberg Foundation, KAW 2005.0098
Note
Updated from submitted to published. QC 20120327Available from: 2009-12-03 Created: 2009-11-28 Last updated: 2012-03-27Bibliographically approved
In thesis
1. 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
2. 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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  • apa
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