Geometry Analysis And Probability
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Geometry Analysis And Probability
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Author : Jean-Benoît Bost
language : fr
Publisher: Birkhäuser
Release Date : 2017-04-26
Geometry Analysis And Probability written by Jean-Benoît Bost and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-26 with Mathematics categories.
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.
Geometry Analysis And Probability
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Author : Jean-Benoît Bost
language : en
Publisher:
Release Date : 2017
Geometry Analysis And Probability written by Jean-Benoît Bost and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Distribution (Probability theory) categories.
Introduction To Geometric Probability
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Author : Daniel A. Klain
language : en
Publisher: Cambridge University Press
Release Date : 1997-12-11
Introduction To Geometric Probability written by Daniel A. Klain and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-11 with Mathematics categories.
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.
Analysis And Geometry Of Markov Diffusion Operators
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Author : Dominique Bakry
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-18
Analysis And Geometry Of Markov Diffusion Operators written by Dominique Bakry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-18 with Mathematics categories.
The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
Stochastic And Integral Geometry
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Author : Rolf Schneider
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-08
Stochastic And Integral Geometry written by Rolf Schneider and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-08 with Mathematics categories.
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.
Differential Geometry And Statistics
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Author : M.K. Murray
language : en
Publisher: Routledge
Release Date : 2017-10-19
Differential Geometry And Statistics written by M.K. Murray and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
Engaging Mathematics
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Author : Melissa Agnew
language : en
Publisher:
Release Date : 2012-08-24
Engaging Mathematics written by Melissa Agnew and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-24 with categories.
Based on the popularity of the original Engaging Math book, Kagan how offers this rich array of ready-go-do activities for the geometry and data analysis & probability strands. You'll find interactive Kagan Structures for pair work, teamwork, and whole-class engagement. Geometry activities cover; shapes and their attributes, edges, faces, vertices, symmetry, congruent, similar, transformations, angels, points, lines, segments, rays, parallel, perpendicular, and intersecting. Data Analysis & Probability activities cover: picture graphs,line graphs, bar graphs, line plots, charts, pie graphs, directional maps and grids, coordinate grids, mean, median, mode, data and probability. Engaging Math just got easier.
Geometric Modeling In Probability And Statistics
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Author : Ovidiu Calin
language : en
Publisher: Springer
Release Date : 2014-08-01
Geometric Modeling In Probability And Statistics written by Ovidiu Calin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Mathematics categories.
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.
Analysis And Probability
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Author : Palle E. T. Jorgensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-17
Analysis And Probability written by Palle E. T. Jorgensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-17 with Mathematics categories.
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. —John von Neumann While this is a course in analysis, our approach departs from the beaten path in some ways. Firstly, we emphasize a variety of connections to themes from neighboring fields, such as wavelets, fractals and signals; topics typically not included in a gradu ate analysis course. This in turn entails excursions into domains with a probabilistic flavor. Yet the diverse parts of the book follow a common underlying thread, and to gether they constitute a good blend; each part in the mix naturally complements the other. In fact, there are now good reasons for taking a wider view of analysis, for ex ample the fact that several applied trends have come to interact in new and exciting ways with traditional mathematical analysis—as it was taught in graduate classes for generations. One consequence of these impulses from "outside" is that conventional boundaries between core disciplines in mathematics have become more blurred. Fortunately this branching out does not mean that students will need to start out with any different or additional prerequisites. In fact, the ideas involved in this book are intuitive, natural, many of them visual, and geometric. The required background is quite minimal and it does not go beyond what is typically required in most graduate programs.
Fractals In Probability And Analysis
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Author : Christopher J. Bishop
language : en
Publisher: Cambridge University Press
Release Date : 2017
Fractals In Probability And Analysis written by Christopher J. Bishop and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.