Random Fields And Geometry

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Random Fields and Geometry

R. J. Adler,Jonathan E. Taylor
Random Fields and Geometry Book PDF

Author : R. J. Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 50,6 Mb
Release : 2009-01-29
Category : Mathematics
ISBN : 9780387481166

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Random Fields and Geometry by R. J. Adler,Jonathan E. Taylor Pdf

This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.

The Geometry of Random Fields

Robert J. Adler
The Geometry of Random Fields Book PDF

Author : Robert J. Adler
Publisher : SIAM
Page : 295 pages
File Size : 40,6 Mb
Release : 2010-01-28
Category : Mathematics
ISBN : 9780898716931

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The Geometry of Random Fields by Robert J. Adler Pdf

An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.

Stochastic Geometry, Spatial Statistics and Random Fields

Volker Schmidt
Stochastic Geometry Spatial Statistics and Random Fields Book PDF

Author : Volker Schmidt
Publisher : Springer
Page : 464 pages
File Size : 42,9 Mb
Release : 2014-10-24
Category : Mathematics
ISBN : 9783319100647

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Stochastic Geometry, Spatial Statistics and Random Fields by Volker Schmidt Pdf

This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.

Stochastic Geometry, Spatial Statistics and Random Fields

Evgeny Spodarev
Stochastic Geometry Spatial Statistics and Random Fields Book PDF

Author : Evgeny Spodarev
Publisher : Springer
Page : 446 pages
File Size : 52,7 Mb
Release : 2013-02-11
Category : Mathematics
ISBN : 9783642333057

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Stochastic Geometry, Spatial Statistics and Random Fields by Evgeny Spodarev Pdf

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

Spatiotemporal Random Fields

George Christakos
Spatiotemporal Random Fields Book PDF

Author : George Christakos
Publisher : Elsevier
Page : 696 pages
File Size : 40,8 Mb
Release : 2017-07-26
Category : Science
ISBN : 9780128030325

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Spatiotemporal Random Fields by George Christakos Pdf

Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others. The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty. Contains applications in the form of examples and case studies, providing readers with first-hand experiences Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas Includes significant updates from the previous edition, including a focus on new theoretical and applied results

Random Fields and Their Geometry

Robert J. Adler
Random Fields and Their Geometry Book PDF

Author : Robert J. Adler
Publisher : Unknown
Page : 456 pages
File Size : 42,9 Mb
Release : 2005-04-30
Category : Mathematics
ISBN : 0817641548

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Random Fields and Their Geometry by Robert J. Adler Pdf

This self-contained monograph contains a number of topics that focus on the many developments in the area of mathematical probability/statistics known as random fields. Robert Adler has been one of the major contributors to this subject. In an earlier work (1981) he dealt with a wide variety of geometrical problems that are unique to stochastic processes in dimensions higher than one, fashioning an interesting blend of geometry and probability. Some old classical topics (non-geometric in nature) are presented in the first few chapters, but the material has been recast in the post-1980 setting of entropy. This is followed by a treatment of random geometry which takes into account the recent work by Worsley et al, and a significant update on our understanding of the fractal nature of erratic random fields. The geometric theme of the book is carried throughout in a user- friendly style. As in his previous work, Adler engages scientists outside of pure and applied mathematics, in particular, researchers involved in brain imaging, and astrophysicists. Applications of excursion set theory in astrophysics and brain imaging are detailed in a short chapter.It is hope that the approach employed in these two quite different areas will direct the reader to finding applications elsewhere. In recent years, the geometry of random fields has also found its way into the literature of materials (surface) science, oceanography, and geology. For applications in the medical community, a chapter discussing the tube formula approach involves the geometry on manifolds and an examination of the distribution of the maximum of Gaussian random

Level Sets and Extrema of Random Processes and Fields

Jean-Marc Azais,Mario Wschebor
Level Sets and Extrema of Random Processes and Fields Book PDF

Author : Jean-Marc Azais,Mario Wschebor
Publisher : John Wiley & Sons
Page : 407 pages
File Size : 44,5 Mb
Release : 2009-02-17
Category : Mathematics
ISBN : 9780470434635

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Level Sets and Extrema of Random Processes and Fields by Jean-Marc Azais,Mario Wschebor Pdf

A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts of stochastic processes, including a modern review of Gaussian fields and their classical inequalities. Subsequent chapters are devoted to Rice formulas, regularity properties, and recent results on the tails of the distribution of the maximum. Finally, applications of random fields to various areas of mathematics are provided, specifically to systems of random equations and condition numbers of random matrices. Throughout the book, applications are illustrated from various areas of study such as statistics, genomics, and oceanography while other results are relevant to econometrics, engineering, and mathematical physics. The presented material is reinforced by end-of-chapter exercises that range in varying degrees of difficulty. Most fundamental topics are addressed in the book, and an extensive, up-to-date bibliography directs readers to existing literature for further study. Level Sets and Extrema of Random Processes and Fields is an excellent book for courses on probability theory, spatial statistics, Gaussian fields, and probabilistic methods in real computation at the upper-undergraduate and graduate levels. It is also a valuable reference for professionals in mathematics and applied fields such as statistics, engineering, econometrics, mathematical physics, and biology.

Random Fields for Spatial Data Modeling

Dionissios T. Hristopulos
Random Fields for Spatial Data Modeling Book PDF

Author : Dionissios T. Hristopulos
Publisher : Springer Nature
Page : 884 pages
File Size : 45,6 Mb
Release : 2020-02-17
Category : Science
ISBN : 9789402419184

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Random Fields for Spatial Data Modeling by Dionissios T. Hristopulos Pdf

This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.

Stochastic Geometry

David Coupier
Stochastic Geometry Book PDF

Author : David Coupier
Publisher : Springer
Page : 232 pages
File Size : 43,7 Mb
Release : 2019-04-09
Category : Mathematics
ISBN : 9783030135478

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Stochastic Geometry by David Coupier Pdf

This volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications.

Geometry, Analysis and Probability

Jean-Benoît Bost,Helmut Hofer,François Labourie,Yves Le Jan,Xiaonan Ma,Weiping Zhang
Geometry Analysis and Probability Book PDF

Author : Jean-Benoît Bost,Helmut Hofer,François Labourie,Yves Le Jan,Xiaonan Ma,Weiping Zhang
Publisher : Birkhäuser
Page : 361 pages
File Size : 42,5 Mb
Release : 2017-04-26
Category : Mathematics
ISBN : 9783319496382

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Geometry, Analysis and Probability by Jean-Benoît Bost,Helmut Hofer,François Labourie,Yves Le Jan,Xiaonan Ma,Weiping Zhang Pdf

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.

High-Dimensional Probability

Roman Vershynin
High Dimensional Probability Book PDF

Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 49,9 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781108415194

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High-Dimensional Probability by Roman Vershynin Pdf

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Tensor-Valued Random Fields for Continuum Physics

Anatoliy Malyarenko,Martin Ostoja-Starzewski
Tensor Valued Random Fields for Continuum Physics Book PDF

Author : Anatoliy Malyarenko,Martin Ostoja-Starzewski
Publisher : Cambridge University Press
Page : 313 pages
File Size : 52,9 Mb
Release : 2018-12-06
Category : Science
ISBN : 9781108429856

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Tensor-Valued Random Fields for Continuum Physics by Anatoliy Malyarenko,Martin Ostoja-Starzewski Pdf

Presents a complete description of homogenous and isotropic tensor-valued random fields, including the problems of continuum physics, mathematical tools and applications.

Stochastic and Integral Geometry

Rolf Schneider,Wolfgang Weil
Stochastic and Integral Geometry Book PDF

Author : Rolf Schneider,Wolfgang Weil
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 54,7 Mb
Release : 2008-09-08
Category : Mathematics
ISBN : 9783540788591

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Stochastic and Integral Geometry by Rolf Schneider,Wolfgang Weil Pdf

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.

Information Geometry

Geert Verdoolaege
Information Geometry Book PDF

Author : Geert Verdoolaege
Publisher : MDPI
Page : 355 pages
File Size : 41,6 Mb
Release : 2019-04-04
Category : Juvenile Nonfiction
ISBN : 9783038976325

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Information Geometry by Geert Verdoolaege Pdf

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.

The Generic Chaining

Michel Talagrand
The Generic Chaining Book PDF

Author : Michel Talagrand
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 52,9 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783540274995

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The Generic Chaining by Michel Talagrand Pdf

The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov. It takes the reader from the first principles to the edge of current knowledge and to the open problems that remain in this domain.