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Singularities of gaussian random maps into the plane

Singularities of gaussian random maps into the plane We compute the expected value of various quantities related to the biparametric singularities of a pair of smooth centered Gaussian random fields on an n-dimensional compact manifold, such as the lengths of the critical curves and contours of a fixed index and the number of cusps. We obtain certain expressions under no particular assumptions other than smoothness of the two fields, but more explicit formulae are derived under varying levels of additional constraints such as the two random fields being i.i.d, stationary, isotropic etc. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied and Computational Topology Springer Journals

Singularities of gaussian random maps into the plane

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Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
2367-1726
eISSN
2367-1734
DOI
10.1007/s41468-023-00113-0
Publisher site
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Abstract

We compute the expected value of various quantities related to the biparametric singularities of a pair of smooth centered Gaussian random fields on an n-dimensional compact manifold, such as the lengths of the critical curves and contours of a fixed index and the number of cusps. We obtain certain expressions under no particular assumptions other than smoothness of the two fields, but more explicit formulae are derived under varying levels of additional constraints such as the two random fields being i.i.d, stationary, isotropic etc.

Journal

Journal of Applied and Computational Topology – Springer Journals

Published: Mar 3, 2023

Keywords: Persistent homology; Biparametric persistence; Gaussian random fields; 55N31; 62R40; 60G15

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