LEADER 03284nam 22006495 450 001 9910484788603321 005 20250331124709.0 010 $a9783642195808 010 $a3642195806 024 7 $a10.1007/978-3-642-19580-8 035 $a(CKB)2670000000084124 035 $a(SSID)ssj0000506052 035 $a(PQKBManifestationID)11313334 035 $a(PQKBTitleCode)TC0000506052 035 $a(PQKBWorkID)10513525 035 $a(PQKB)11021969 035 $a(DE-He213)978-3-642-19580-8 035 $a(MiAaPQ)EBC3066734 035 $a(PPN)153863099 035 $a(EXLCZ)992670000000084124 100 $a20110516d2011 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTopological Complexity of Smooth Random Functions $eÉcole d'Été de Probabilités de Saint-Flour XXXIX-2009 /$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 $aÉcole d'Été de Probabilités de Saint-Flour ;$v2019 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642195792 311 08$a3642195792 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 ;$v2019 606 $aGeometry 606 $aStatistics 606 $aGeometry 606 $aStatistical Theory and Methods 615 0$aGeometry. 615 0$aStatistics. 615 14$aGeometry. 615 24$aStatistical Theory and Methods. 676 $a519.23 700 $aAdler$b Robert J$0103626 701 $aTaylor$b Jonathan$01229526 712 12$aEcole d'ete de probabilites de Saint-Flour. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484788603321 996 $aTopological complexity of smooth random functions$94197033 997 $aUNINA