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Stochastic Geometry: Percolation, Tesselations, Gaussian Fields and Point Processes

  • Book
  • Jul 2025

Overview

Editors:
  1. Hermine Biermé

    1. Institut Denis Poisson, Tours University, Tours, France

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  • Offers comprehensive insights into cutting-edge stochastic geometry research and applications
  • Features contributions from leading experts, blending theory with practical applications
  • Covers diverse topics, including percolation, Gaussian fields, and signal processing

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2365)

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About this book

This volume covers a broad spectrum of topics in stochastic geometry, including percolation, tessellations, Gaussian fields and point processes. Based on lectures given at the Stochastic Geometry Days held by the Stochastic Geometry Research Group from 2019 to 2022, the book opens with an introduction to Russo–Seymour–Welsh theory for the study of percolation, before going on to explore random tessellations and their applications, the geometry of Gaussian random fields, and the zeros of analytic Gaussian fields. This discussion naturally leads to the concept of determinantal point processes, whose applications in signal processing are the focus of the final chapter. Providing a unique and accessible overview of active fields in stochastic geometry, their tools and models, this collection of lectures will encourage further research and applications.

Keywords

  • Stochastic Geometry
  • Percolation
  • Gaussian Random Fields
  • Determinantal Processes
  • Tesselation

Editors and Affiliations

  • Institut Denis Poisson, Tours University, Tours, France

    Hermine Biermé

About the editor

Hermine Biermé is responsible for the Stochastic Geometry Research Group (RT CNRS INSMI 3477), a national research structure funded by the CNRS, established in 2012, that aims to unite the French community working in this field. Since 2014, its annual meetings have been preceded by introductory courses for graduate students, postdocs, and researchers looking to delve into stochastic geometry. Five of the initial lectures from 2014 to 2017 were compiled in the book "Stochastic Geometry: Modern Research Frontiers" (2019), edited by David Coupier, in the "CEMPI Subseries" of Springer’s Lecture Notes in Mathematics.

Bibliographic Information

  • Book Title: Stochastic Geometry: Percolation, Tesselations, Gaussian Fields and Point Processes

  • Editors: Hermine Biermé

  • Series Title: Lecture Notes in Mathematics

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2025

  • Softcover ISBN: 978-3-031-87263-1Due: 01 August 2025

  • eBook ISBN: 978-3-031-87264-8Due: 01 August 2025

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIII, 234

  • Number of Illustrations: 90 b/w illustrations, 27 illustrations in colour

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