Variance of the volume of random real algebraic submanifolds II
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Publication:5113783
DOI10.1512/iumj.2019.68.7830zbMath1440.53067arXiv1707.09771OpenAlexW4292500492WikidataQ126565887 ScholiaQ126565887MaRDI QIDQ5113783
Thomas Letendre, Martin Puchol
Publication date: 17 June 2020
Published in: Indiana University Mathematics Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1707.09771
Bergman kernelKac-Rice formulalinear statisticsWiener-Ito expansionreal projective manifoldsrandom submanifoldsKostlan-Shub-Smale polynomials
Random fields (60G60) Global submanifolds (53C40) Real algebraic and real-analytic geometry (14P99) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)
Related Items
Central limit theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems ⋮ Asymptotic variance of the number of real roots of random polynomial systems ⋮ Zeros of smooth stationary Gaussian processes ⋮ Roots of Kostlan polynomials: moments, strong law of large numbers and central limit theorem
Cites Work
- Unnamed Item
- Expected volume and Euler characteristic of random submanifolds
- Betti numbers of random real hypersurfaces and determinants of random symmetric matrices
- Non-universality of nodal length distribution for arithmetic random waves
- Number variance of random zeros on complex manifolds. II: Smooth statistics
- Exponential rarefaction of real curves with many components
- Multiple Wiener-Itô integral expansions for level-crossing-count functionals
- Distribution of zeros of random and quantum chaotic sections of positive line bundles
- Quantum chaotic dynamics and random polynomials
- Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes
- Universality and scaling of correlations between zeros on complex manifolds
- \(C^\infty\) scaling asymptotics for the spectral projector of the Laplacian
- Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights
- Nodal length fluctuations for arithmetic random waves
- Phase singularities in complex arithmetic random waves
- Holomorphic Morse inequalities and Bergman kernels
- Critical sets of random smooth functions on compact manifolds
- Exponential estimate for the asymptotics of Bergman kernels
- Normal Approximations with Malliavin Calculus
- Asymptotic Laws for the Spatial Distribution and the Number of Connected Components of Zero Sets of Gaussian Random Functions
- Variance of the volume of random real algebraic submanifolds
- EXPECTED TOPOLOGY OF RANDOM REAL ALGEBRAIC SUBMANIFOLDS
- Level Sets and Extrema of Random Processes and Fields
- Bergman kernels and equilibrium measures for line bundles over projective manifolds
- Asymptotic variance of the number of real roots of random polynomial systems
- Local Universality of Zeroes of Random Polynomials
- Random Fields and Geometry
- Real algebraic surfaces
- On the asymptotic expansion of Bergman kernel
- Central limit theorems for level functionals of stationary Gaussian processes and fields
- Asymptotic variance and CLT for the number of zeros of Kostlan Shub Smale random polynomials
