New Perspectives in Stochastic Geometry
Wilfrid S. Kendall and Ilya Molchanov
Abstract
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 sch ... More
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 seventeen 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.
Keywords:
stochastic geometry,
random patterns,
probability theory,
statistics,
image analysis,
material science,
fractals,
percolation theory,
randomized allocation
Bibliographic Information
| Print publication date: 2009 |
Print ISBN-13: 9780199232574 |
| Published to Oxford Scholarship Online: February 2010 |
DOI:10.1093/acprof:oso/9780199232574.001.0001 |
Authors
Affiliations are at time of print publication.
Wilfrid S. Kendall, editor
Department of Statistics, University of Warwick, UK
Ilya Molchanov, editor
Department of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland
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