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Topological Complexity of Smooth Random Functions - Ecole d'Ete de Probabilites de Saint-Flour XXXIX-2009 (Paperback, 2011)
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Topological Complexity of Smooth Random Functions - Ecole d'Ete de Probabilites de Saint-Flour XXXIX-2009 (Paperback, 2011)
Series: Lecture Notes in Mathematics, 2019
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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.
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