Spatial Stochastic Processes A Festschrift in Honor of Ted Harris on
This volume has been created in honor of the seventieth birthday of Ted Harris, which was celebrated on January 11th, 1989. The papers rep resent the wide range of subfields of probability theory in which Ted has made profound and fundamental contributio
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Series Editors Thomas Liggett Charles Newman Loren Pitt
Spatial Stochastic Processes A Festschrift in Honor of Ted Harris on his Seventieth Birthday Kenneth s. Alexander Joseph C. Watkins Editors
Springer Science+Business Media, LLC
Joseph C. Watkins Department of Mathematics University of Southem Califomia Los Angeles, CA 90089-1113
Kenneth S. Alexander Department of Mathematics University of Southem Califomia Los Angeles, CA 90089-1113
Library of Congress Cataloguing-in-Publication:Data Spatial stochastic processes : a festschrift in honor of Ted Harris on his seventieth birthday / Kenneth S. Alexander, Joseph C. Watkins, editors. p. cm. -- (Progress in probability : 19) Includes bibliographical references. ISBN 978-1-4612-6766-9
ISBN 978-1-4612-0451-0 (eBook)
DOI 10.1007/978-1-4612-0451-0
1. Stochastic processes. 2. Spatial analysis (Statistics) 3. Harris, Theodore Edward, 1919- . I. Harris, Theodore Edwards, 11. Alexander, Kenneth S. III. Walkins, Joseph C. 1919IV. Series. 89-18290 QA274.S65 1990 519.2--dc20 CIP Printed on acid-free paper.
© Springer Science+Business Media New York 1991 Originally published by Birkhäuser Boston in 1991 Softcover reprint of the hardcover 1st edition 1991 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system,or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner.
ISBN 978-1-4612-6766-9
Typeset by Authors in TeX.
987654321
Table of Contents
Branching Processes P. Ney, Branching Random Walk
J. T. Cox, Some Remarks on the Theory of Critical Branching Random Walk Percolation D. J. Barsky, G. R. Grimmett and C. Newman, Dynamic Renormalization and Continuity of the Percolation Transitions in Orthants H. Kesten, Asymptotics in High Dimensions for the Fortuin-Kasteleyn Random Cluster Model
3
23
37 57
Interacting Particle Systems
R. Holley, On the Asymptotics of the Spin-Spin Autocorrelation Function
89
in Stochastic Ising Models Near the Critical Temperature T. M. Liggett, Spatially Inhomogeneous Contact Processes
105
R. Durrett, A New Method for Proving the Existence of Phase Transitions
141
R. Fisch, J. Gravner and D. Griffeath, Cyclic Cellular Automata in Two Dimensions
171
Stochastic Flows P. Baxendale, Statistical Equilibrium and Two-Point Motion for a Stochastic Flow of Diffeomorphisms
189
Y. Le Jan, Asymptotic Properties of Isotropic Brownian Flows
219
H. Kunita, Ergodic Properties of Nonlinear Filtering Processes
233
Preface This volume has been created in honor of the seventieth birthday of Ted Harris, which was celebrated on January 11th, 1989. The papers represent the wide range of subfields of probability theory in which Ted has made profound and fundamental contributions. This breadth in Ted's research complicates the task of putting together in his honor a book with a unified theme. One common thread noted was the spatial, or geometric, aspect of the phenomena Ted investigated. This volume has b
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