On Probability Measures with Unbounded Angular Ratio

The angular ratio is an important characteristic of probability measures on \(\mathbb{Z}\) in the theory of ergodic dynamical systems. Answering the J. Rosenblatt question, we describe probability measures whose spectrum is not inside some Stolz region at

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Peter Eichelsbacher · Guido Elsner Holger Kösters · Matthias Löwe Franz Merkl · Silke Rolles Editors

Limit Theorems in Probability, Statistics and Number Theory

Springer Proceedings in Mathematics and Statistics Volume 42

For further volumes: http://www.springer.com/series/10533

Springer Proceedings in Mathematics and Statistics

This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including OR and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today.

Peter Eichelsbacher  Guido Elsner Holger K¨osters  Matthias L¨owe  Franz Merkl Silke Rolles Editors

Limit Theorems in Probability, Statistics and Number Theory In Honor of Friedrich G¨otze

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Editors Peter Eichelsbacher Mathematics Faculty Ruhr-University Bochum Bochum Germany

Guido Elsner Mathematics Faculty Bielefeld University Bielefeld Germany

Holger K¨osters Mathematics Faculty Bielefeld University Bielefeld Germany

Matthias L¨owe Institute for Mathematical statistics University of M¨unster M¨unster Germany

Franz Merkl Mathematics Institute University of M¨unchen M¨unchen Germany

Silke Rolles Centre for Mathematics Technische Universit¨at M¨unchen Garching bei M¨unchen Germany

ISSN 2194-1009 ISSN 2194-1017 (electronic) ISBN 978-3-642-36067-1 ISBN 978-3-642-36068-8 (eBook) DOI 10.1007/978-3-642-36068-8 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013936545 Mathematical Subject Classification (2010): 60F05, 62E20, 60-06, 46L54, 60B20, 60E10, 11J83 c Springer-Verlag Berlin Heidelberg 2013  This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liab

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