Geometric Probability
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| Author | : Daniel A. Klain |
| Publisher | : Cambridge University Press |
| Total Pages | : 196 |
| Release | : 1997-12-11 |
| Genre | : Mathematics |
| ISBN | : 9780521596541 |
The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.
| Author | : Herbert Solomon |
| Publisher | : SIAM |
| Total Pages | : 180 |
| Release | : 1978-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970418 |
Topics include: ways modern statistical procedures can yield estimates of pi more precisely than the original Buffon procedure traditionally used; the question of density and measure for random geometric elements that leave probability and expectation statements invariant under translation and rotation; the number of random line intersections in a plane and their angles of intersection; developments due to W.L. Stevens's ingenious solution for evaluating the probability that n random arcs of size a cover a unit circumference completely; the development of M.W. Crofton's mean value theorem and its applications in classical problems; and an interesting problem in geometrical probability presented by a karyograph.
| Author | : Ovidiu Calin |
| Publisher | : Springer |
| Total Pages | : 389 |
| Release | : 2014-07-17 |
| Genre | : Mathematics |
| ISBN | : 3319077791 |
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.
| Author | : Jean-Benoît Bost |
| Publisher | : Birkhäuser |
| Total Pages | : 363 |
| Release | : 2017-04-26 |
| Genre | : Mathematics |
| ISBN | : 3319496387 |
This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.
| Author | : V.V. Buldygin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 322 |
| Release | : 2000-08-31 |
| Genre | : Mathematics |
| ISBN | : 9780792364139 |
This book demonstrates the usefulness of geometric methods in probability theory and mathematical statistics, and shows close relationships between these disciplines and convex analysis. Deep facts and statements from the theory of convex sets are discussed with their applications to various questions arising in probability theory, mathematical statistics, and the theory of stochastic processes. The book is essentially self-contained, and the presentation of material is thorough in detail. Audience: The topics considered in the book are accessible to a wide audience of mathematicians, and graduate and postgraduate students, whose interests lie in probability theory and convex geometry.
| Author | : Maurice George Kendall |
| Publisher | : |
| Total Pages | : 136 |
| Release | : 1963 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Mathew Penrose |
| Publisher | : Oxford University Press |
| Total Pages | : 345 |
| Release | : 2003 |
| Genre | : Computers |
| ISBN | : 0198506260 |
This monograph provides and explains the mathematics behind geometric graph theory. Applications of this theory are used on the study of neural networks, spread of disease, astrophysics and spatial statistics.
| Author | : Herbert Solomon |
| Publisher | : SIAM |
| Total Pages | : 180 |
| Release | : 1978-06-01 |
| Genre | : Mathematics |
| ISBN | : 0898710251 |
Topics include: ways modern statistical procedures can yield estimates of pi more precisely than the original Buffon procedure traditionally used; the question of density and measure for random geometric elements that leave probability and expectation statements invariant under translation and rotation; and much more.
| Author | : Rolf Schneider |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 692 |
| Release | : 2008-09-08 |
| Genre | : Mathematics |
| ISBN | : 354078859X |
Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.
| Author | : A.M. Mathai |
| Publisher | : CRC Press |
| Total Pages | : 580 |
| Release | : 1999-12-01 |
| Genre | : Mathematics |
| ISBN | : 9789056996819 |
A useful guide for researchers and professionals, graduate and senior undergraduate students, this book provides an in-depth look at applied and geometrical probability with an emphasis on statistical distributions. A meticulous treatment of geometrical probability, kept at a level to appeal to a wider audience including applied researchers who will find the book to be both functional and practical with the large number of problems chosen from different disciplines A few topics such as packing and covering problems that have a vast literature are introduced here at a peripheral level for the purpose of familiarizing readers who are new to the area of research.
