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 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 been organized around that theme, with papers covering four major subject areas of Ted's research: branching processes, percola tion, interacting particle systems, and stochastic flows. These four topics do not· exhaust his research interests; his major work on Markov chains is commemorated in the standard technology "Harris chain" and "Harris recurrent" . The editors would like to take this opportunity to thank the speakers at the symposium and the contributors to this volume. Their enthusi astic support is a tribute to Ted Harris. We would like to express our appreciation to Annette Mosley for her efforts in typing the manuscripts and to Arthur Ogawa for typesetting the volume. Finally, we gratefully acknowledge the National Science Foundation and the University of South ern California for their financial support.
Table of ContentsBranching Processes.- Branching Random Walk.- Some Remarks on the Theory of Critical Branching Random Walk.- Percolation.- Dynamic Renormalization and Continuity of the Percolation Transitions in Orthants.- Asymptotics in High Dimensions for the Fortuin-Kasteleyn Random Cluster Model.- Interacting Particle Systems.- On the Asymptotics of the Spin-Spin Autocorrelation Function in Stochastic Ising Models Near the Critical Temperature.- Spatially Inhomogeneous Contact Processes.- A New Method for Proving the Existence of Phase Transitions.- Cyclic Cellular Automata in Two Dimensions.- Stochastic Flows.- Statistical Equilibrium and Two-Point Motion for a Stochastic Flow of Diffeomorphisms.- Asymptotic Properties of Isotropic Brownian Flows.- Ergodic Properties of Nonlinear Filtering Processes.