Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields

DOI10.1007/s10958-014-1844-9zbMath1339.60038arXiv1206.0371OpenAlexW1969429658MaRDI QIDQ2253979

Dmitry Zaporozhets, Zakhar Kabluchko

Publication date: 16 February 2015

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0371

zbMATH Keywords

ellipsoidsBernstein theoremWishart matrixKac-Rice formulamixed volumesGaussian random fieldsGaussian random determinantGaussian random parallelotope

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Geometric probability and stochastic geometry (60D05) Random matrices (probabilistic aspects) (60B20)

Related Items (7)

Exclusion volumes of convex bodies in high space dimensions: applications to virial coefficients and continuum percolation ⋮ How many roots of a system of random Laurent polynomials are real? ⋮ Convex hulls of multidimensional random walks ⋮ Matrix Hermite polynomials, random determinants and the geometry of Gaussian fields ⋮ Crofton formulae for products ⋮ Random affine simplexes ⋮ Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls

Cites Work

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• The number of roots of a system of equations
• Computing mixed discriminants, mixed volumes, and permanents
• Moment-generating operators for determinants of product moments in samples from a normal system
• Stochastic and Integral Geometry
• The Distribution of the Determinant of a Complex Wishart Distributed Matrix

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