Stochastic geometry and its applications. 3rd revised and extended ed.

*(English)*Zbl 1291.60005
Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons (ISBN 978-0-470-66481-0/hbk). xxvi, 544 p. (2013).

Since the appearance of its first edition in 1987 [Zbl 0622.60019], this monograph has been a major source of reference and inspiration for several generations of applied probabilists interested in spatial random structures. A particular feature of this book is its interest and accessibility for the readers of various backgrounds: from pure probabilists and geometers to researchers working in material science, microscopy and image analysis. The carefully chosen presentation level balances between the mathematical rigour and applied intuition supported by numerous examples.

In 1987 this was one of the first books in the area of stochastic geometry. Since then there appeared numerous special monographs emphasising convex and integral geometry, tessellations, the statistical theory of shape, stereology, the theory of point processes, random sets, and spatial statistics – each of these areas mentioned in the first edition has witnessed vigorous developments over the last decades. The book under review provides an ideal entrance point to the considerable literature on the stochastic geometry where full proofs and numerous extensions of the presented results can be found.

The monograph under review covers all main topics in stochastic geometry: point processes, random sets, random measures, line and fibre processes, random tessellations, geometrical networks and graphs, stereology. The current edition incorporates many developments in stochastic geometry since 1995, including new results on point processes, random graphs and their applications, new tessellation models, to name the few. To free some space, the authors decided to leave out the chapter on random shapes, covered by a sufficient number of other monographs. The new edition contains over 700 new references, while about 300 outdated references have been deleted.

The new edition is recommended for institutional libraries and personal collections of researches interested in the accessible and nicely written monograph on the modern stochastic geometry with emphasis on applications. I am sure that this book will retain its importance in stochastic geometry and spatial statistics for many years to come.

In 1987 this was one of the first books in the area of stochastic geometry. Since then there appeared numerous special monographs emphasising convex and integral geometry, tessellations, the statistical theory of shape, stereology, the theory of point processes, random sets, and spatial statistics – each of these areas mentioned in the first edition has witnessed vigorous developments over the last decades. The book under review provides an ideal entrance point to the considerable literature on the stochastic geometry where full proofs and numerous extensions of the presented results can be found.

The monograph under review covers all main topics in stochastic geometry: point processes, random sets, random measures, line and fibre processes, random tessellations, geometrical networks and graphs, stereology. The current edition incorporates many developments in stochastic geometry since 1995, including new results on point processes, random graphs and their applications, new tessellation models, to name the few. To free some space, the authors decided to leave out the chapter on random shapes, covered by a sufficient number of other monographs. The new edition contains over 700 new references, while about 300 outdated references have been deleted.

The new edition is recommended for institutional libraries and personal collections of researches interested in the accessible and nicely written monograph on the modern stochastic geometry with emphasis on applications. I am sure that this book will retain its importance in stochastic geometry and spatial statistics for many years to come.

Reviewer: Ilya S. Molchanov (Bern)

##### MSC:

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

60D05 | Geometric probability and stochastic geometry |

62M30 | Inference from spatial processes |

60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |