title: Distribution of the Height of Local Maxima of Gaussian Random Fields.
abstract: Let {f(t) :t∈T} be a smooth Gaussian random field over a parameter spaceT, whereTmay be a subset of Euclidean space or, more generally, a Riemannian manifold. We provide a general formula for the distribution of the height of a local maximum [Formula: see text] is a local maximum off(t)} whenfis non-stationary. Moreover, we establish asymptotic approximations for the overshoot distribution of a local maximum [Formula: see text] is a local maximum off(t) andf(t0) >v} asv→ ∞. Assuming further thatfis isotropic, we apply techniques from random matrix theory related to the Gaussian orthogonal ensemble to compute such conditional probabilities explicitly whenTis Euclidean or a sphere of arbitrary dimension. Such calculations are motivated by the statistical problem of detecting peaks in the presence of smooth Gaussian noise.
authors.affiliation: North Carolina State University.
authors.forename: Dan
authors.initials: D
authors.lastname: Cheng
authors.affiliation: North Carolina State University.
authors.forename: Armin
authors.initials: A
authors.lastname: Schwartzman
keywords: Euler characteristic; Gaussian orthogonal ensemble; Height; Riemannian manifold; isotropic field; local maxima; overshoot; sphere