Progress in High-Dimensional Percolation and Random Graphs
This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open
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Markus Heydenreich Remco van der Hofstad
Progress in HighDimensional Percolation and Random Graphs
CRM Short Courses Series Editor Galia Dafni, Concordia University, Montreal, QC, Canada
Editorial Board Mireille Bousquet-Mélou (CNRS, LaBRI, Université de Bordeaux) Antonio Córdoba Barba (ICMAT, Universidad Autónoma de Madrid) Svetlana Jitomirskaya (UC Irvine) V. Kumar Murty (University of Toronto) Leonid Polterovich (Tel Aviv University)
The volumes in the CRM Short Courses series have a primarily instructional aim, focusing on presenting topics of current interest to readers ranging from graduate students to experienced researchers in the mathematical sciences. Each text is aimed at bringing the reader to the forefront of research in a particular area or field, and can consist of one or several courses with a unified theme. The inclusion of exercises, while welcome, is not strictly required. Publications are largely but not exclusively, based on schools, instructional workshops and lecture series hosted by, or affiliated with, the Centre de Researches Mathématiques (CRM). Special emphasis is given to the quality of exposition and pedagogical value of each text.
More information about this series at http://www.springer.com/series/15360
Markus Heydenreich Remco van der Hofstad
Progress in High-Dimensional Percolation and Random Graphs
Markus Heydenreich Mathematisches Institut Ludwig-Maximilians-Universität München Munich, Bayern Germany
Remco van der Hofstad Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven The Netherlands
CRM Short Courses ISBN 978-3-319-62472-3 ISBN 978-3-319-62473-0 (eBook) DOI 10.1007/978-3-319-62473-0 Library of Congress Control Number: 2017945258 Mathematics Subject Classification (2010): 60K35, 60K37, 82B43 © Springer International Publishing Switzerland 2017 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. The publisher remains neutral with regard to jurisdictional claims in published maps and in
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