The Gauss-Bonnet-Chern theorem: a probabilistic perspective

2014/04/21 by Nicolaescu, Liviu I., Savale, Nikhil · 1 citation
#35P20 #53C65 #58J35 #58J40 #58J50 #60D05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1404.5206

Abstract

We prove that the Euler form of a metric connection on real oriented vector bundle E over a compact oriented manifold M can be identified, as a current, with the expectation of the random current defined by the zero-locus of a certain random section of the bundle. We also explain how to reconstruct probabilistically the metric and the connection on E from the statistics of random sections of E.

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