Expected volume and Euler characteristic of random submanifolds

DOI10.1016/j.jfa.2016.01.007zbMath1349.58007arXiv1408.2107OpenAlexW1553728973MaRDI QIDQ255880

Thomas Letendre

Publication date: 9 March 2016

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.2107

zbMATH Keywords

Euler characteristicrandom polynomialreal projective manifoldRiemannian random wave

Mathematics Subject Classification ID

Random fields (60G60) Geometric probability and stochastic geometry (60D05) Integration on manifolds; measures on manifolds (58C35) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Topology of real algebraic varieties (14P25) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (18)

Equidistribution of the conormal cycle of random nodal sets ⋮ Weighted local Weyl laws for elliptic operators ⋮ Universal components of random nodal sets ⋮ Expected number and distribution of critical points of real Lefschetz pencils ⋮ Asymptotic topology of excursion and nodal sets of Gaussian random fields ⋮ Random colorings in manifolds ⋮ Variance of the volume of random real algebraic submanifolds II ⋮ Necessary and sufficient conditions for the finiteness of the second moment of the measure of level sets ⋮ Percolation of random nodal lines ⋮ Random knots in 3-dimensional 3-colour percolation: numerical results and conjectures ⋮ Universality of the nodal length of bivariate random trigonometric polynomials ⋮ Asymptotic variance of the number of real roots of random polynomial systems ⋮ Roots of Kostlan polynomials: moments, strong law of large numbers and central limit theorem ⋮ Restriction of 3D arithmetic Laplace eigenfunctions to a plane ⋮ Nodal intersections for arithmetic random waves against a surface ⋮ Variance of the volume of random real algebraic submanifolds ⋮ Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension \(d\geq 3\) ⋮ Almost-sure asymptotics for Riemannian random waves

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