Singularities of Gaussian Random Maps into the Plane
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 ndimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2022
 arXiv:
 arXiv:2202.08242
 Bibcode:
 2022arXiv220208242K
 Keywords:

 Mathematics  Probability;
 Mathematics  Geometric Topology