New Perspectives in Stochastic Geometry

Edited by Wilfrid S. Kendall, Department of Statistics, University of Warwick, UK, and Ilya Molchanov, Department of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland

Contributors:

Pierre Calka; Ignacio Cascos; Antonio Cuevas; Ricardo Fraiman; Wilfrid S. Kendall; Günter Last; Huiling Le; Klaus Mecke; Ilya Molchanov; Jesper Møller; Peter Mörters; Werner Nagel; Mathew D. Penrose; Matthias Reitzner; Rolf Schneider; Tomasz Schreiber; Remco van der Hofstad; Marei-Colette N.M. van Lieshout; Andrew R. Wade; Wolfgang Weil; Sergei Zuyev

Published by Oxford University Press, January 2010.

The book can now be ordered from Amazon.

608 pages | 40 illustrations | 234x156mm
978-0-19-923257-4 | Hardback

* Expounds current developments in the area of stochastic geometry
* 17 chapters by leading researchers in the area
* Accessible to graduate students

Stochastic Geometry is a subject with roots stretching back at least 300 years, but one which has only been formed as an academic area in the last 50 years. It covers the study of random patterns, their probability theory, and the challenging problems raised by their statistical analysis. It has grown rapidly in response to challenges in all kinds of applied science, from image analysis through to materials science. Recently, still more stimulus has arisen from exciting new links with rapidly developing areas of mathematics, from fractals through percolation theory to randomized allocation schemes. Coupled with many ongoing developments arising from all sorts of applications, the area is changing and developing rapidly. This book is intended to lay foundations for future research directions, by collecting together 17 chapters contributed by leading researchers in the field, both theoreticians and people involved in applications, surveying these new developments both in theory and in applications. It will introduce and lay foundations for appreciating the fresh perspectives, new ideas and interdisciplinary connections now arising from Stochastic Geometry and from other areas of mathematics now connecting to this area. This will benefit young researchers wishing to gain quick access to the area, scientists from other fields wanting perspectives on what the area has to offer their own speciality, and workers already active in the field who will enjoy and profit from the coverage of a wide and rapidly developing field.

Readership: Graduates and researchers in mathematics and probability.

List of Contents

Preface

1: Rolf Schneider & Wolfgang Weil: Classical stochastic geometry

I NEW DEVELOPMENTS IN CLASSICAL STOCHASTIC GEOMETRY

2: Matthias Reitzner: Random polytopes
3: Günter Last: Modern random measures: Palm theory and related models
4: Tomasz Schreiber: Limit theorems in stochastic geometry
5: Pierre Calka: Tessellations

II STOCHASTIC GEOMETRY AND MODERN PROBABILITY

6: Remco van der Hofstad: Percolation and random graphs
7: Mathew D. Penrose & Andrew R. Wade: Random directed and on-line networks
8: Peter Mörters: Random fractals

III STATISTICS AND STOCHASTIC GEOMETRY

9: Jesper Møller: Inference
10: Wilfrid S. Kendall & Huiling Le: Statistical shape theory
11: Antonio Cuevas & Ricardo Fraiman: Set estimation
12: Ignacio Cascos: Data depth: multivariate statistics and geometry

IV APPLICATIONS

13: Marie-Colette N.M. van Lieshout: Applications of stochastic geometry in image analysis
14: Werner Nagel: Stereology
15: Klaus Mecke: Physics of spatially structured materials
16: Sergei Zuyev: Stochastic geometry and telecommunications networks
17: Ilya Molchanov: Random sets in finance and econometrics

Index

List of Errata:

(none yet reported)