000			02889nam a22004815i 4500
001			978-3-642-19580-8
003			DE-He213
005			20140220083757.0
007			cr nn 008mamaa
008			110516s2011 gw | s |||| 0|eng d
020			_a9783642195808 _9978-3-642-19580-8
024	7		_a10.1007/978-3-642-19580-8 _2doi
050		4	_aQA440-699
072		7	_aPBM _2bicssc
072		7	_aMAT012000 _2bisacsh
082	0	4	_a516 _223
100	1		_aAdler, Robert J. _eauthor.
245	1	0	_aTopological Complexity of Smooth Random Functions _h[electronic resource] : _bÉcole d'Été de Probabilités de Saint-Flour XXXIX-2009 / _cby Robert J. Adler, Jonathan E. Taylor.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2011.
300			_aVIII, 122 p. 15 illus., 9 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes in Mathematics, _x0075-8434 ; _v2019
505	0		_a1 Introduction -- 2 Gaussian Processes -- 3 Some Geometry and Some Topology -- 4 The Gaussian Kinematic Formula -- 5 On Applications: Topological Inference -- 6 Algebraic Topology of Excursion Sets: A New Challenge.
520			_aThese notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
650		0	_aMathematics.
650		0	_aGeometry.
650		0	_aMathematical statistics.
650	1	4	_aMathematics.
650	2	4	_aGeometry.
650	2	4	_aStatistical Theory and Methods.
700	1		_aTaylor, Jonathan E. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642195792
830		0	_aLecture Notes in Mathematics, _x0075-8434 ; _v2019
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-19580-8
912			_aZDB-2-SMA
912			_aZDB-2-LNM
999			_c107585 _d107585