Perplexing Problems in Probability Festschrift in Honor of Harry Kes
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Series Editors Thomas Liggett Charles Newman Loren Pitt
Perplexing Problems in Probability Festschrift in Honor of Harry Kesten Maury Bramson Rick Durrett Editors
Birkhauser Boston • Basel • Berlin
Maury Bramson School of Mathematics University of Minnesota Minneapolis, MN 55455
Rick Durrett Department of Mathematics Cornell University Ithaca, NY 14853
Library of Congress Cataloging-In-Publication Data PeIplexing problems in probability : festschrift in honor of Harry Kesten I Maury Bramson, Rick T. Durrett, editors. p. cm. - (Progress in probability ; v.44) ISBN-13: 978-1-4612-7442-1 e-ISBN-13: 978-1-4612-2168-5 DOl: 10.1007/978-1-4612-2168-5 1. Probabilities. I. Kesten, Harry, 1931- . II. Bramson, . IV. Series: Maury, 1951- . m. Durrett, Richard, 1951Progress in probability ; 44. QA273.l8.P47 1999 519.2--dc21 99-14285 CIP
AMS Subject Classifications: 6OF05, 6OFI0, 6OE07, 60025,60007,60110,60115, 60K25, 60K35, 62G30, 52AI0, 82B20 Printed on acid-free paper. 1999 Birkhiiuser Boston Birkhiiuser Softcover reprint of the hardcover 1st edition 1999 @
All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhiiuser Boston, clo Springer-Vedag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief exceIpts in connection with reviews or scholarly analysis. Use In connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. ISBN-13: 978-1-4612-7442-1 Formatted from authors' files by TEXniques, Inc., Cambridge, MA.
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Harry Kesten
Dedicated to Harry Kesten In honor of 40 years of impressive research accomplishments in probability
Contents
1 Harry Kesten's Publications: A Personal Perspective Rick Durrett . ....................................................... 1 2
Lattice Trees, Percolation and Super-Brownian Motion
3
Percolation in 00 + 1 Dimensions at the Uniqueness Threshold
4
Percolation on Transitive Graphs as a Coalescent Process: Relentless Merging Followed by Simultaneous Uniqueness
Gordon Slade . .................................................... 35 Roberto H. Schonmann . ............................................ 53
Olle Haggstrom, Yuval Peres, and Roberto H. Schonmann ............. 69 5
Inequalities and Entanglements for Percolation and Random-Cluster Models
Geoffrey R. Grimmett .............................................. 91
6
From Greedy Lattice Animals to Euclidean First-Passage Percolation
C. Douglas Howard and Charles M. Newman ....................... 107
7
Reverse Shapes in First-Passage Percolation and Related Growth Models
Janko Gravner and Davi
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