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 RussoSeymourWelsh 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.
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1. An Introduction to Russo-Seymour-Welsh Theory.-
2. Random
Tessellations - An Overview of Models.-
3. Gaussian Fields through
Geometrical Properties.-
4. Complex Gaussian Zeros and Eigenvalues.-
5. Point
Processes and Spatial Statistics in Time-Frequency Analysis.
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 Springers Lecture Notes in Mathematics.
