A stochastic Gauss-Bonnet-Chern formula

DOI10.1007/s00440-015-0630-zzbMath1346.35140arXiv1408.5746OpenAlexW2040633291MaRDI QIDQ292125

Liviu I. Nicolaescu

Publication date: 10 June 2016

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.5746

zbMATH Keywords

curvaturecurrentsconnectionsGaussian measuresGauss-Bonnet-Chern theoremKac-Rice formulaEuler formrandom sections

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Pseudodifferential and Fourier integral operators on manifolds (58J40) Integral geometry (53C65) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

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A CLT concerning critical points of random functions on a Euclidean space, The Gauss-Bonnet-Chern theorem: A probabilistic perspective, Counting Zeros of Random Functions, Random fields and the enumerative geometry of lines on real and complex hypersurfaces, Kac-Rice formula for transverse intersections

Cites Work

• A note on the Gauss-Bonnet-Chern theorem for general connection
• Stochastic local Gauss-Bonnet-Chern theorem
• Processus linéaires, processus généralisés
• The Gauss-Bonnet-Chern theorem: A probabilistic perspective
• Level Sets and Extrema of Random Processes and Fields
• Gaussian Measures on Function Spaces
• On the small balls problem for equivalent Gaussian measures
• Random Fields and Geometry
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