Asymptotic laws for the spatial distribution and the number of connected components of zero sets of Gaussian random functions
arXiv:1507.02017
Abstract
We study the asymptotic laws for the spatial distribution and the number of connected components of zero sets of smooth Gaussian random functions of several real variables. The primary examples are various Gaussian ensembles of real-valued polynomials (algebraic or trigonometric) of large degree on the sphere or torus, and translation-invariant smooth Gaussian functions on the Euclidean space restricted to large domains.
References in corpus (8)
- Percolation model for nodal domains of chaotic wave functions
- An Introduction to Stochastic PDEs
- Random wave functions and percolation
- On the number of connected components of random algebraic hypersurfaces
- Universal components of random nodal sets
- Statistics on Hilbert's Sixteenth Problem
- On the topology of the zero sets of monochromatic random waves
- Non-universality of the Nazarov-Sodin constant