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Birkhäuser

Random Walks, Brownian Motion, and Interacting Particle Systems

A Festschrift in Honor of Frank Spitzer

  • Book
  • © 1991

Overview

Editors:
  1. Rick Durrett

    1. Department of Mathematics, Cornell University, Ithaca, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Harry Kesten

    1. Department of Mathematics, Cornell University, Ithaca, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Probability (PRPR, volume 28)

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xii
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  2. Reprints of Frank Spitzer

    1. Front Matter

      Pages 1-1
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    2. A Combinatorial Lemma and its Application to Probability Theory

      • Frank Spitzer
      Pages 3-19

    3. Some Theorems Concerning 2-Dimensional Brownian Motion

      • Frank Spitzer
      Pages 21-31

    4. Recurrent Random Walk and Logarithmic Potential

      • Frank Spitzer
      Pages 33-52

    5. Electrostatic Capacity, Heat Flow, and Brownian Motion

      • Frank Spitzer
      Pages 53-65

    6. Interaction of Markov Processes

      • Frank Spitzer
      Pages 66-110

  3. Papers Dedicated to Frank Spitzer

    1. Front Matter

      Pages 111-111
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    2. A Useful Renormalization Argument

      • Maury Bramson, Lawrence Gray
      Pages 113-152

    3. Capture Problems For Coupled Random Walks

      • Maury Bramson, David Griffeath
      Pages 153-188

    4. Nonlinear Voter Models

      • J. T. Cox, R. Durrett
      Pages 189-201

    5. On the Long Term Behavior of Finite Particle Systems: A Critical Dimension Example

      • J. T. Cox, Andreas Greven
      Pages 203-213

    6. Large Deviation Lower Bounds For General Sequences Of Random Variables

      • A. deAcosta, P. Ney, E. Nummelin
      Pages 215-221

    7. Asymptotic Laplace-Transforms

      • Hermann Dinges
      Pages 223-230

    8. Higher Order Hydrodynamic Equations for a System of Independent Random Walks

      • R. Dobrushin, F. Sokolovskii
      Pages 231-254

    9. Making Money From Fair Games

      • R. Durrett, H. Kesten, G. Lawler
      Pages 255-267

    10. Additive Functionals of Superdiffusion Processes

      • E. B. Dynkin
      Pages 269-281

    11. Interacting Systems, Stirrings, and Flows

      • T. E. Harris
      Pages 283-293

    12. The One Dimensional Stochastic X-Y Model

      • Richard Holley
      Pages 295-307

    13. Relations Between Solutions to a Discrete and Continuous Dirichlet Problem

      • Harry Kesten
      Pages 309-321
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Keywords

About this book

This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come. Frank has always liked new phenomena, clean formulations and elegant proofs. He has created or opened up several research areas and it is not surprising that many people are still working out the consequences of his inventions. By way of introduction we have reprinted some of Frank's seminal articles so that the reader can easily see for himself the point of origin for much of the research presented here. These articles of Frank's deal with properties of Brownian motion, fluctuation theory and potential theory for random walks, and, of course, interacting particle systems. The last area was started by Frank as part of the general resurgence of treating problems of statistical mechanics with rigorous probabilistic tools.

Editors and Affiliations

  • Department of Mathematics, Cornell University, Ithaca, USA

    Rick Durrett, Harry Kesten

Bibliographic Information

  • Book Title: Random Walks, Brownian Motion, and Interacting Particle Systems

  • Book Subtitle: A Festschrift in Honor of Frank Spitzer

  • Editors: Rick Durrett, Harry Kesten

  • Series Title: Progress in Probability

  • DOI: https://doi.org/10.1007/978-1-4612-0459-6

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1991

  • Hardcover ISBN: 978-0-8176-3509-1Published: 01 June 1991

  • Softcover ISBN: 978-1-4612-6770-6Published: 18 October 2012

  • eBook ISBN: 978-1-4612-0459-6Published: 06 December 2012

  • Series ISSN: 1050-6977

  • Series E-ISSN: 2297-0428

  • Edition Number: 1

  • Number of Pages: XII, 455

  • Topics: Probability Theory and Stochastic Processes

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