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130626  eng 
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a 9780387481166

100 
1 

a Adler, R. J.

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0 
0 
a Random Fields and Geometry
h Elektronische Ressource
c by R. J. Adler, Jonathan E. Taylor

250 


a 1st ed. 2007

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a New York, NY
b Springer New York
c 2007, 2007

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a XVIII, 454 p. 21 illus
b online resource

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0 

a Gaussian Processes  Gaussian Fields  Gaussian Inequalities  Orthogonal Expansions  Excursion Probabilities  Stationary Fields  Geometry  Integral Geometry  Differential Geometry  Piecewise Smooth Manifolds  Critical Point Theory  Volume of Tubes  The Geometry of Random Fields  Random Fields on Euclidean Spaces  Random Fields on Manifolds  Mean Intrinsic Volumes  Excursion Probabilities for Smooth Fields  NonGaussian Geometry

653 


a Statistics

653 


a Probability Theory

653 


a Geometry

653 


a Mathematical physics

653 


a Statistics

653 


a Mathematical Methods in Physics

653 


a Probabilities

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1 

a Taylor, Jonathan E.
e [author]

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0 
7 
a eng
2 ISO 6392

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b Springer
a Springer eBooks 2005

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0 

a Springer Monographs in Mathematics

028 
5 
0 
a 10.1007/9780387481166

856 
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0 
u https://doi.org/10.1007/9780387481166?nosfx=y
x Verlag
3 Volltext

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0 

a 519.2

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a 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. The three parts to the monograph are quite distinct. Part I presents a userfriendly yet comprehensive background to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities. Part II gives a quick review of geometry, both integral and Riemannian, to provide the reader with the material needed for Part III, and to give some new results and new proofs of known results along the way. Topics such as Crofton formulae, curvature measures for stratified manifolds, critical point theory, and tube formulae are covered. In fact, this is the only concise, selfcontained treatment of all of the above topics, which are necessary for the study of random fields. The new approach in Part III is devoted to the geometry of excursion sets of random fields and the related Euler characteristic approach to extremal probabilities. "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 selfstudy. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory. These applications, to appear in a forthcoming volume, will cover areas as widespread as brain imaging, physical oceanography, and astrophysics
