Asymptotic laws for the spatial distribution and the number of connected components of zero sets of Gaussian random functions
By Fedor Nazarov, M. Sodin. 2015
169 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d5450b74652caf455eb5ad76b9a34f44dc7eb780
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Percolation of random nodal lines (2016, unknown): “The following Lemma proves the first condition, and is a quantitative version of Lemma 7 in [35].”
- The complexity of spherical p-spin models - a second moment approach (2015, background): “See, for example, Nazarov and Sodin [35, 36] and references therein.”