| 书目名称 | Topological Complexity of Smooth Random Functions | | 副标题 | École d‘Été de Proba | | 编辑 | Robert J. Adler,Jonathan E. Taylor | | 视频video | | | 概述 | The 2007 monograph has been very well received, but does not make for easy reading. The current notes, while not as exhaustive, are much more readable. As such, they provide a comparatively easy entry | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | These 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. | | 出版日期 | Book 2011 | | 关键词 | 60-02, 60G15, 55N35, 60Gxx, 60G60, 53Cxx, 62H35, 60G55, 53C65; Differential topology; Gaussian extrema | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-19580-8 | | isbn_softcover | 978-3-642-19579-2 | | isbn_ebook | 978-3-642-19580-8Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 2011 |
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发表于 2025-3-21 16:44:15
