The Gauss-Bonnet-Chern theorem: A probabilistic perspective
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- by Liviu I. Nicolaescu and Nikhil Savale PDF
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Abstract:
We prove that the Euler form of a metric connection on a 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 $E$.References
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Additional Information
- Liviu I. Nicolaescu
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556-4618
- MR Author ID: 242770
- Email: nicolaescu.1@nd.edu
- Nikhil Savale
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556-4618
- MR Author ID: 1077187
- Email: nsavale@nd.edu
- Received by editor(s): November 21, 2014
- Received by editor(s) in revised form: September 15, 2015, and December 16, 2015
- Published electronically: November 28, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 2951-2986
- MSC (2010): Primary 35P20, 53C65, 58J35, 58J40, 58J50, 60D05
- DOI: https://doi.org/10.1090/tran/6895
- MathSciNet review: 3592534