Quantum Probability and Spectral Analysis of Graphs
This is the first book to comprehensively cover the quantum probabilistic approach to spectral analysis of graphs. This approach has been developed by the authors and has become an interesting research area in applied mathematics and physics. The book can
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Editorial Board W. Beiglböck, Institute of Applied Mathematics, University of Heidelberg, Germany J.-P. Eckmann, Department of Theoretical Physics, University of Geneva, Switzerland H. Grosse, Institute of Theoretical Physics, University of Vienna, Austria M. Loss, School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA S. Smirnov, Mathematics Section, University of Geneva, Switzerland L. Takhtajan, Department of Mathematics, Stony Brook University, NY, USA J. Yngvason, Institute of Theoretical Physics, University of Vienna, Austria
Akihito Hora Nobuaki Obata
Quantum Probability and Spectral Analysis of Graphs With a Foreword by Professor Luigi Accardi
With 48 Figures
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Professor Dr. Akihito Hora
Professor Dr. Nobuaki Obata
Graduate School of Mathematics Nagoya Universtiy Nagoya 464-8602, Japan
Graduate School of Information Sciences Tohoku University Sendai 980-8579, Japan
Akihito Hora and Nobuaki Obata, Quantum Probability and Spectral Analysis of Graphs, Theoretical and Mathematical Physics (Springer, Berlin Heidelberg 2007) DOI 10.1007/b11501497
Library of Congress Control Number: 2006940905 ISSN 0172-5998 ISBN-13 978-3-540-48862-0 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, 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. Typesetting: by the authors and techbooks using a Springer LATEX macro package Cover design: eStudio Calamar, Girona/Spain Printed on acid-free paper
SPIN: 11501497
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Foreword
It is a great pleasure for me that the new Springer Quantum Probability Programme is opened by the present monograph of Akihito Hora and Nobuaki Obata. In fact this book epitomizes several distinctive features of contemporary quantum probability: First of all the use of specific quantum probabilistic techniques to bring original and quite non-trivial contributions to problems with an old history and on which a huge literature exists, both independent of quantum probability. Second, but not less important, the ability to create several bridges among different branches of mathematics apparently far from one another such as the theory of orthogonal polynomials and graph theory, Neva
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