000			04038nam a22004935i 4500
001			978-0-387-48116-6
003			DE-He213
005			20250710084002.0
007			cr nn 008mamaa
008			100301s2007 xxu| s |||| 0|eng d
020			_a9780387481166 _a99780387481166
024	7		_a10.1007/978-0-387-48116-6 _2doi
082	0	4	_a519.2 _223
100	1		_aAdler, Robert J. _eauthor.
245	1	0	_aRandom Fields and Geometry _h[recurso electrónico] / _cby Robert J. Adler, Jonathan E. Taylor.
264		1	_aNew York, NY : _bSpringer New York, _c2007.
300			_aXVII, 448 p. 21 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _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	_aMATHEMATICS.
650		0	_aGEOMETRY.
650		0	_aDISTRIBUTION (PROBABILITY THEORY).
650		0	_aMATHEMATICAL PHYSICS.
650		0	_aSTATISTICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aPROBABILITY THEORY AND STOCHASTIC PROCESSES.
650	2	4	_aSTATISTICS, GENERAL.
650	2	4	_aGEOMETRY.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
700	1		_aTaylor, Jonathan E. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387481128
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-48116-6 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
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