A stochastic Gauss-Bonnet-Chern formula
成果类型：
Article
署名作者：
Nicolaescu, Liviu I.
署名单位：
University of Notre Dame
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-015-0630-z
发表日期：
2016
页码：
235-265
关键词：
摘要：
We prove that a Gaussian ensemble of smooth random sections of a real vector bundle over compact manifold canonically defines a metric on together with a connection compatible with it. Additionally, we prove a refined Gauss-Bonnet theorem stating that if the bundle and the manifold are oriented, then the Euler form of the above connection can be identified, as a current, with the expectation of the random current defined by the zero-locus of a random section in the above Gaussian ensemble.
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