Monochromatic Random Waves for General Riemannian Manifolds
This is a survey article on some of the recent developments on monochromatic random waves defined for general Riemannian manifolds. We discuss the conditions needed for the waves to have a universal scaling limit, we review statistics for the size of thei
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ntiers in Analysis and Probability In the Spirit of the Strasbourg-Zürich Meetings
Frontiers in Analysis and Probability
Nalini Anantharaman • Ashkan Nikeghbali Michael Th. Rassias Editors
Frontiers in Analysis and Probability In the Spirit of the Strasbourg-Z¨urich Meetings
Editors Nalini Anantharaman IRMA University of Strasbourg Strasbourg, France
Ashkan Nikeghbali Institute of Mathematics University of Z¨urich Z¨urich, Switzerland
Michael Th. Rassias Institute of Mathematics University of Z¨urich Z¨urich, Switzerland
ISBN 978-3-030-56408-7 ISBN 978-3-030-56409-4 (eBook) https://doi.org/10.1007/978-3-030-56409-4 Mathematics Subject Classification: 32-XX, 34-XX, 35-XX, 37-XX, 39-XX, 42-XX, 43-XX, 46-XX, 47-XX, 60-XX, 65-XX, 81-XX © Springer Nature Switzerland AG 2020 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, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This volume presents papers devoted to a broad spectrum of areas of Mathematical Analysis and Probability Theory, in the spirit of the topics treated in the so-called Strasbourg–Zürich Meetings. These meetings have been organized twice a year since 2015, taking place once in Zürich and once in Strasbourg each year, and constitute a place of vibrant mathematical communication that gathers experts from all over the world. Topics treated within the scope of this volume include the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp -cohomology (in degree one) of graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH approa
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