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101 0 $aeng
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181   $ctxt
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200 10$aTopological Complexity of Smooth Random Functions$b[electronic resource] $eÉcole d'Été de Probabilités de Saint-Flour XXXIX-2009 /$fby Robert Adler, Jonathan E. Taylor
205   $a1st ed. 2011.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2011.
215   $a1 online resource (VIII, 122 p. 15 illus., 9 illus. in color.)
225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2019
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-19579-2 
320   $aIncludes bibliographical references and indexes.
327   $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.
330   $aThese notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors? 2007 Springer monograph ?Random Fields and Geometry.? While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
410  0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2019
606   $aGeometry
606   $aStatistics 
606   $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006
606   $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001
615  0$aGeometry.
615  0$aStatistics .
615 14$aGeometry.
615 24$aStatistical Theory and Methods.
676   $a519.23
700   $aAdler$b Robert$4aut$4http://id.loc.gov/vocabulary/relators/aut$0103626
702   $aTaylor$b Jonathan E$4aut$4http://id.loc.gov/vocabulary/relators/aut
712 12$aEcole d'e?te? de probabilite?s de Saint-Flour.
906   $aBOOK
912   $a996466613103316
996   $aTopological complexity of smooth random functions$9261806
997   $aUNISA