## Stochastic Geometry: Modern Research Frontiers"This volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications." -- Prové de l'editor. |

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### Contents

1 Some Classical Problems in Random Geometry | 1 |

2 Understanding Spatial Point Patterns Through Intensity and Conditional Intensities | 45 |

3 Stochastic Methods for Image Analysis | 87 |

4 Introduction to Random Fields and Scale Invariance | 129 |

5 Introduction to the Theory of Gibbs Point Processes | 181 |

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### Common terms and phrases

algorithm Appl asymptotic normality bounded central limit theorem Coeurjolly compute configurations connected components consider contrario convex body convex hull covariance function Cox processes defined Definition denote density distribution DLR equations energy function exists finite range finite volume GPP Fourier fractal fractional Brownian fields function H Gaussian field Gaussian random field Gibbs measures Gibbs point processes given GNZ equations Hölder integral integral geometry intensity function interaction isotropic level lines LGCP Math Mathematics matrix maximal meaningful method Mřller noise non-negative obtain pairwise Palm intensity Papangelou conditional intensity parameter parametric estimation percolation pixels point patterns Poisson point process probability problem Proof properties Proposition pseudo-likelihood estimator random measure random variable Sect segments self-similar simulation spatial point processes Stat stationary increments statistical stochastic geometry tessellation texture synthesis Theorem variogram vertices