On Central Limit Theorems in Geometrical Probability (Classic Reprint) - Tapa blanda

Sinopsis

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.

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