Abstract
The nodal densities of gaussian random functions, modelling various physical systems including chaotic quantum eigenfunctions and optical speckle patterns, are reviewed. The nodal domains of isotropically random real and complex functions are formulated in terms of their Minkowski functionals, and their correlations and spectra are discussed. The results on the statistical densities of the zeros of the real and complex functions, and their derivatives, in two dimensions are reviewed. New results are derived on the nodal domains of the hessian determinant (gaussian curvature) of two-dimensional random surfaces.
Translated title of the contribution | Nodal densities of planar gaussian random waves |
---|---|
Original language | English |
Pages (from-to) | 191 - 210 |
Number of pages | 20 |
Journal | European Physical Journal: Special Topics |
Volume | 145 |
DOIs | |
Publication status | Published - Jun 2007 |