The giant component of excursion sets of spherical Gaussian ensembles: existence, uniqueness, and volume concentration
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DOI: 10.1007/s00440-025-01367-8
Abstract: We establish the existence and uniqueness of a well-concentrated giant component in the supercritical excursion sets of three important ensembles of spherical Gaussian random fields: Kostlan’s ensemble, band-limited ensembles, and the random spherical harmonics. Our… read more here.
Keywords: excursion; giant component; spherical gaussian; existence uniqueness ... See more keywords
Identification and isotropy characterization of deformed random fields through excursion sets
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DOI: 10.1017/apr.2018.32
Abstract: Abstract A deterministic application θ:ℝ2→ℝ2 deforms bijectively and regularly the plane and allows the construction of a deformed random field X∘θ:ℝ2→ℝ from a regular, stationary, and isotropic random field X:ℝ2→ℝ. The deformed field X∘θ is,… read more here.
Keywords: excursion; field; deformed random; identification isotropy ... See more keywords
Lipschitz-Killing curvatures of excursion sets for two-dimensional random fields
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DOI: 10.1214/19-ejs1530
Abstract: In the present paper, we study three geometric characteristics for the excursion sets of a two dimensional stationary random field. First we show that these characteristics can be estimated without bias if the considered field… read more here.
Keywords: excursion sets; considered field; random; sets two ... See more keywords