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In the theory of stationary spatial point processes, Palm distributions are used to describe the point process seen from one of its points. Such an intrinsic frame of reference is not only interesting for theoretical considerations, but also useful in related fields such as queuing theory and stochastic geometry.

Stochastic geometry.

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In the theory of stationary spatial point processes, Palm distributions are used to describe the point process seen from one of its points. Such an intrinsic frame of reference is not only interesting for theoretical considerations, but also useful in related fields such as queuing theory and stochastic geometry.

Stochastic geometry.

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Stochastic geometry --- Géométrie stochastique.

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This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate non-trivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a non-specialist audience. Even in the later chapters, where the factorisation principles are applied to geometrical processes, the prerequisites are only standard courses on probability and analysis. The main ideas presented here have application to such areas as stereology and tomography, geometrical statistics, pattern and texture analysis. This book will be well suited as a starting point for individuals working in those areas to learn about the mathematical framework. It will also prove valuable as an introduction to geometric probability theory and integral geometry based on modern ideas.

Stochastic geometry. --- Geometric probabilities. --- Factorization (Mathematics) --- Mathematics --- Probabilities --- Geometry --- Stochastic geometry --- Geometric probabilities

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Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results.

Wireless communication systems --- Stochastic models. --- Stochastic geometry. --- Mathematics.