Perturbation of Linear Forms of Singular Vectors Under Gaussian Noise
Let \(A \in \mathbb{R}^{m\times n}\) be a matrix of rank r with singular value decomposition (SVD) A = ∑k = 1 r σ k (u k ⊗ v k ), where {σ k , k = 1, …, r} are singular values of A (arranged in a non-increasing order) and \(u_{k} \in \mathbb{R}^{m},v_{k}
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Christian Houdré David M. Mason Patricia Reynaud-Bouret Jan Rosin´ski Editors
High Dimensional Probability VII The Cargèse Volume
Progress in Probability Volume 71 Series Editors Steffen Dereich Davar Khoshnevisan Andreas E. Kyprianou Sidney I. Resnick
More information about this series at http://www.springer.com/series/4839
Christian Houdré • David M. Mason • Patricia Reynaud-Bouret • Jan Rosi´nski Editors
High Dimensional Probability VII The CargJese Volume
Editors Christian Houdré Georgia Institute of Technology Atlanta, GA, USA
David M. Mason University of Delaware Department of Applied Economics and Statistics Newark, DE, USA
Patricia Reynaud-Bouret Université Côte d’Azur Centre national de la recherche scientifique Laboratoire J.A. Dieudonné Nice, France
ISSN 1050-6977 Progress in Probability ISBN 978-3-319-40517-9 DOI 10.1007/978-3-319-40519-3
Jan Rosi´nski Department of Mathematics University of Tennessee Knoxville, TN, USA
ISSN 2297-0428 (electronic) ISBN 978-3-319-40519-3 (eBook)
Library of Congress Control Number: 2016953111 Mathematics Subject Classification (2010): 60E, 60G15, 52A40, 60E15, 94A17, 60F05, 60K35, 60C05, 05A05, 60F17, 62E17, 62E20, 60J05, 15B99, 15A18, 47A55, 15B52 © Springer International Publishing Switzerland 2016 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. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser, www.birkhauser-science.com The registered company is Springer International Publishing AG
Preface
The High-Dimensional Probability proceedings continue a well-established tradition which began with the series of eight International Conferences on Probability in Banach Spaces, starting with Oberwolfach in 1975. An earlier conference on Gaussian processes with many of the same participants as the 1975 meeting was held in Strasbourg in 1973. The last Banach space meeting took place in Bowdoin, Maine, in 1991. It was decided in 1994 that, in order to reflect the widening audience and interests
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