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RANDOM FIELDS AND GEOMETRY

Foundations and Case Studies

Robert J. Adler, Jonathan E. Taylor and Keith J. Worsley

This under-production book is being written with a statistical audience in mind. It will contain a brief review of the theory of Random Fields and Geometry (see below) with some additions that are of more practical importance. More significantly, it will go into detail as to how to apply the theory in practice, along with a slew of examples.

As the book progesses we shall post early versions here, on the understanding that since it is a work in progress you should expect errors and oversights.

We shall be very grateful for all comments, questions, suggestions and lists of typos that will help improve the final version.

In the meantime, one click will download the first four chapters for you. These are mainly background theory chapters. The rest should start appearing soon.

RANDOM FIELDS AND GEOMETRY

Robert J. Adler and Jonathan E. Taylor

This book was published by Springer in mid-2007. Go here (for Europe) or here (for USA) for details. It is written in three parts, and here are some details:

Preface

Contents

PART I: GAUSSIAN PROCESSES

PART II: GEOMETRY

PART III: GEOMETRY OF RANDOM FIELDS

Index

For preprints of specific chapters, please write directly to me.

Go here for a CORRECTION LIST .

For those of you who downloaded earlier versions of the entire book, you should note that the final published version has material that was in none of the web versions and also has far fewer errors. (We would like to say "no further errors" but are not that optimistic.) So, be sure to run out and order yourself a copy of the published volume as well.

We thank all those who read the earlier versions and sent us their lists of errors.

RECENT PREPRINTS

  • R.J. Adler, G. Samorodnitsky and J.E. Taylor, High level excursion set geometry for non-Gaussian infinitely divisible random fields
  • R.J. Adler,  J. Ewing and P. Taylor, Citation Statistics: A report from the International Mathematical Union  in  cooperation with the International Council of Industrial and  Applied Mathematics  and the Institute of Mathematical  Statistics
  • R.J. Adler, J. Blanchet and J. Liu, Efficient simulation for tail probabilities of Gaussian random fields
  • R.J. Adler, Some new random field tools for spatial analysis
  • R.J. Adler, G. Samorodnitsky and J.E. Taylor, Excursion sets of stable random fields
  • J.E. Taylor and R.J. Adler, Gaussian processes, kinematic formulae and Poincare's limit
  • G. Bonnet and R.J. Adler, The Burgers superprocess
  • S. Vadlamani and R.J. Adler, Global geometry under isotropic Brownian flows
  • A. Zeevi, R. Meir and R.J. Adler, Non-linear models for time series using mixtures of autoregressive models

    BOOKS

  • R.J. Adler, (1981), The Geometry of Random Fields, Wiley, London. xi+275.

  • R.J. Adler, (1990), , An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, IMS Lecture Notes-Monograph Series, Vol 12, vii + 160. Corrections to Chapter 2 can be found here .

  • R.J. Adler, P. Muller, and B. Rozovskii, (eds), Stochastic Modelling in Physical Oceanography, Birkhaüser, Boston.

  • R.J. Adler, R. Feldman, M. Taqqu, (eds) (1998), A Users Guide to Heavy Tails: Statistical Techniques for Analysing Heavy Tailed Distributions and Processes, Birkhaüser, Boston.

  • R.J. Adler and J.E. Taylor, (2007) Random Fields and Geometry, Springer, Boston.

    MOVIE AND COMPUTER PACKAGE

    Superprocesses: The Movie. A 15-minute video of superprocess visualisations.

    The movie was produced at the Technion Visualization Centre . Drop me a line at robert@ieadler.technion.ac.il and I will mail you a CD with all the mpeg files, or download some now, for simulations of simple superprocesses in one , two , or three dimensions. (In each one of these simulations you will first see a simulation of many particles following a simple random walk, with total mass spreading out according to the discrete heat equation with small random perturbation, followed by branching random walks meant to simulate superprocesses.)

  • SUPER, an interactive C/GL graphics package for the visualisation of superprocesses in dimensions one through five.

    Documentation, including information on how to obtain, run, and, if necessary, compile the programs, is here. 

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