## Stochastic Geometry and Wireless Networks, Volume 1Stochastic Geometry and Wireless Networks, Part I: Theory first provides a compact survey on classical stochastic geometry models, with a main focus on spatial shot-noise processes, coverage processes and random tessellations. It then focuses on signal to interference noise ratio (SINR) stochastic geometry, which is the basis for the modeling of wireless network protocols and architectures considered in Stochastic Geometry and Wireless Networks, Part II: Applications. It also contains an appendix on mathematical tools used throughout Stochastic Geometry and Wireless Networks, Parts I and II. |

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### Contents

Preface | 1 |

Marked Point Processes and ShotNoise Fields | 43 |

Boolean Model | 71 |

Voronoi Tessellation | 91 |

Bibliographical Notes on Part I | 103 |

Interacting SignaltoInterference Ratio Cells | 131 |

SignaltoInterference Ratio Coverage | 137 |

SignaltoInterference Ratio Connectivity | 155 |

Bibliographical Notes on Part II | 165 |

Stationary Marked Point Processes | 175 |

Fairness and Optimality | 181 |

Graph Theoretic Notions | 189 |

199 | |

206 | |

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Assume assumption ball bond percolation Boolean model bounded capacity functional Chapter closed sets conditional distribution Consider constant convergence Corollary coverage process deﬁned Deﬁnition denote density diﬀerent distribution function edge equal ergodic Euclidean space Example ﬁrst ﬁxed formula given graph hoc network homogeneous BM homogeneous Poisson p.p. i.m. Poisson p.p. independently marked inﬁnite connected component intensity measure Laplace transform Lebesgue measure Lemma locally ﬁnite marked p.p. marked point process nodes non-negative Note OPL function p.p. with intensity parameter path-loss Poisson p.p. Poisson point process Proof Proposition radius random closed set random variable Rayleigh fading Remark response function satisﬁed Section shot-noise SINR cell SINR coverage site percolation spherical grains square integrable stationary p.p. stochastic geometry subset suﬃciently Theorem tion transmitters typical cell vector volume fraction Voronoi cell Voronoi tessellation wireless network