Local maxima of Gaussian fields

Expected Number of Local Maxima of Some Gaussian Random Polnomials

expected number of local maxima of some gaussian random polnomials

Distribution of the Height of Local Maxima of Gaussian Random Fields.

Let {f(t) : t ∈ T} be a smooth Gaussian random field over a parameter space T, where T may 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 of f(t)} when f is non-stationary. Moreover, we establish asymptotic approximations for the overshoot distribu...

The Distribution of Maxima of Approximately Gaussian Random Fields

Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown “location” (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an approximation for the tail of the distribution. For the motivating class of problems this gives approximately the significance level of the maximum score test. The m...

Expected Number of Local Maxima of Some Gaussian Random Polynomials

Let Qn(x) = ∑n i=0 Aix i be a random algebraic polynomial where the coefficients A0, A1, · · · form a sequence of centered Gaussian random variables. Moreover, assume that the increments ∆j = Aj − Aj−1, j = 0, 1, 2, · · · are independent, A−1 = 0. The coefficients can be considered as n consecutive observations of a Brownian motion. We study the asymptotic behaviour of the expected number of lo...