Synopsis
Explore how randomness shapes geometry and learn how central limit theorems explain it.
This book (or edition) presents central limit theorems for three geometric problems built on random points: the nearest neighbor graph, the Voronoi diagram, and the Delaunay triangulation. It uses a Poisson model to make the analysis tractable and shows how local dependence leads to universal normal behavior as the number of points grows. The authors compare previous, heavier methods with a simple geometric approach that works well across these problems and highlights connections to algorithm design.
- See how a geometrical framework yields CLTs via local dependence and dependency graphs.
- Understand why Voronoi and Delaunay structures relate to the nearest-neighbor graph and what that implies for computation.
- Learn about the Poisson model, key limits, and how constants can be computed explicitly.
- Discover practical implications for sequential and parallel algorithms on randomly distributed points.
Ideal for readers of probabilistic geometry and computational geometry, those curious about how randomness governs spatial structures and what this means for real-world algorithms.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Autres éditions populaires du même titre
Résultats de recherche pour On Central Limit Theorems in Geometrical Probability...
Image fournie par le vendeur
On Central Limit Theorems in Geometrical Probability (Classic Reprint)
impression à la demandeVendeur : Forgotten Books, London, Royaume-Uni
Évaluation du vendeur 4 sur 5 étoiles
Paperback. Etat : New. Print on Demand. This book presents a significant development in geometrical probability, proving central limit theorems for three fundamental constructions in computational geometry: the k-nearest graph, the Voronoi diagram, and the Delaunay triangulation. Within this field, the author provides a novel approach using dependency graphs to capture local dependence in these problems. The book establishes that, given a Poisson point process with parameter n, the lengths of these graphs satisfy central limit theorems as n approaches infinity. These results provide a theoretical framework for understanding the asymptotic behavior of these graphs and have implications for designing more efficient algorithms for solving related problems. Additionally, the author explores the relationship between these central limit theorems and efficient algorithms for these problems, demonstrating the potential for faster sequential and parallel algorithms. Overall, this book offers a valuable contribution to geometrical probability and computational geometry, providing new insights into the asymptotic behavior of important combinatorial structures and paving the way for advancements in algorithmic design. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N° de réf. du vendeur 9781334015205_0
Acheter neuf
EUR 15,45
Livraison gratuite
Expédition depuis Royaume-Uni vers Etats-Unis
Expédition depuis Royaume-Uni vers Etats-Unis
Quantité disponible : Plus de 20 disponibles
Image d'archives
On Central Limit Theorems in Geometrical Probability Classic Reprint
Vendeur : PBShop.store US, Wood Dale, IL, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781334015205
Acheter neuf
EUR 24,64
Livraison gratuite
Expédition nationale : Etats-Unis
Expédition nationale : Etats-Unis
Quantité disponible : 15 disponible(s)
Image d'archives
On Central Limit Theorems in Geometrical Probability Classic Reprint
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781334015205
Acheter neuf
EUR 23,99
Expédition à EUR 3,82
Expédition depuis Royaume-Uni vers Etats-Unis
Expédition depuis Royaume-Uni vers Etats-Unis
Quantité disponible : 15 disponible(s)