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001 978-0-387-48116-6
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008 100301s2007 xxu| s |||| 0|eng d
020 _a9780387481166
_9978-0-387-48116-6
024 7 _a10.1007/978-0-387-48116-6
_2doi
040 _aISI Library, Kolkata
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
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082 0 4 _a519.2
_223
100 1 _aAdler, Robert J.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aRandom Fields and Geometry
_h[electronic resource] /
_cby Robert J. Adler, Jonathan E. Taylor.
264 1 _aNew York, NY :
_bSpringer New York,
_c2007.
300 _aXVIII, 454 p. 21 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x1439-7382
505 0 _aGaussian 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 -- Non-Gaussian Geometry.
520 _aThis 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 user-friendly 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, self-contained 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 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. These applications, to appear in a forthcoming volume, will cover areas as widespread as brain imaging, physical oceanography, and astrophysics.
650 0 _aDistribution (Probability theory.
650 0 _aStatistics.
650 0 _aGeometry.
650 0 _aMathematical physics.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aStatistics, general.
_0http://scigraph.springernature.com/things/product-market-codes/S0000X
650 2 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
700 1 _aTaylor, Jonathan E.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387564470
776 0 8 _iPrinted edition:
_z9781441923691
776 0 8 _iPrinted edition:
_z9780387481128
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttps://doi.org/10.1007/978-0-387-48116-6
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c425434
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