Asymptotic topology of excursion and nodal sets of Gaussian random fields
Asymptotic topology of excursion and nodal sets of Gaussian random fields
Abstract Let M be a compact smooth manifold of dimension n with or without boundary, or an affine polytope, and let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>f</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mi>M</m:mi> <m:mo>→</m:mo> <m:mi>ℝ</m:mi> </m:mrow> </m:mrow> </m:math> {f:M\to\mathbb{R}} be a smooth Gaussian random field. It is very natural to suppose that for a large …