2019/01/25 by Dmitry Beliaev, Beliaev, Dmitry, Stephen Muirhead +3
Earth and Planetary Sciences · Mathematics · #60B10 #60F99 #FOS: Mathematics #Geology and Paleoclimatology Research #Geometry and complex manifolds #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1901.09000
openalex publication_date 2019/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study in depth the nesting graph and volume distribution of the nodal\ndomains of a Gaussian field, which have been shown in previous works to exhibit\nasymptotic laws. A striking link is established between the asymptotic mean\nconnectivity of a nodal domain (i.e. the vertex degree in its nesting graph)\nand the positivity of the percolation probability of the field, along with a\ndirect dependence of the average nodal volume on the percolation probability.\nOur results support the prevailing ansatz that the mean connectivity and volume\nof a nodal domain is conserved for generic random fields in dimension d=2 but\nnot in d \≥ 3, and are applied to a number of concrete motivating examples.\n