Growth and Isoperimetric Profile of Planar Graphs
In this section we review a joint work with Panos Papasoglu, see [BP11 ], in which the following is proved:
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École d'Été de Probabilités de Saint-Flour
Itai Benjamini
Coarse Geometry and Randomness École d’Été de Probabilités de Saint-Flour XLI – 2011
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis (Zurich) Mario Di Bernardo (Bristol) Alessio Figalli (Pisa/Austin) Davar Khoshnevisan (Salt Lake City) Ioannis Kontoyiannis (Athens) Gabor Lugosi (Barcelona) Mark Podolskij (Heidelberg) Sylvia Serfaty (Paris and NY) Catharina Stroppel (Bonn) Anna Wienhard (Heidelberg)
For further volumes: http://www.springer.com/series/304
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Saint-Flour Probability Summer School
The Saint-Flour volumes are reflections of the courses given at the Saint-Flour Probability Summer School. Founded in 1971, this school is organised every year by the Laboratoire de Mathématiques (CNRS and Université Blaise Pascal, Clermont-Ferrand, France). It is intended for PhD students, teachers and researchers who are interested in probability theory, statistics, and in their applications. The duration of each school is 13 days (it was 17 days up to 2005), and up to 70 participants can attend it. The aim is to provide, in three highlevel courses, a comprehensive study of some fields in probability theory or Statistics. The lecturers are chosen by an international scientific board. The participants themselves also have the opportunity to give short lectures about their research work. Participants are lodged and work in the same building, a former seminary built in the 18th century in the city of Saint-Flour, at an altitude of 900 m. The pleasant surroundings facilitate scientific discussion and exchange. The Saint-Flour Probability Summer School is supported by: – Université Blaise Pascal – Centre National de la Recherche Scientifique (C.N.R.S.) – Ministère délégué à l’Enseignement supérieur et à la Recherche For more information, see back pages of the book and http://math.univ-bpclermont.fr/stflour/ Jean Picard Summer School Chairman Laboratoire de Mathématiques Université Blaise Pascal 63177 Aubière Cedex France
Itai Benjamini
Coarse Geometry and Randomness École d’Été de Probabilités de Saint-Flour XLI – 2011
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Itai Benjamini Department of Mathematics The Weizmann Institute of Science Rehovot, Israel
ISBN 978-3-319-02575-9 ISBN 978-3-319-02576-6 (eBook) DOI 10.1007/978-3-319-02576-6 Springer Cham Heidelberg New York Dordrecht London Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2013953863 Mathematics Subject Classification (2010): 82B43, 82B41, 05C81, 05C10, 05C80 © Springer International Publishing Switzerland 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 sof
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