Expected number of nodal components for cut‐off fractional Gaussian fields

Expected Number of Local Maxima of Some Gaussian Random Polnomials

expected number of local maxima of some gaussian random polnomials

Expected Number and Height Distribution of Critical Points of Smooth Isotropic Gaussian Random Fields

Abstract: We obtain formulae for the expected number and height distribution of critical points of general smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense that there are no restrictions on the covariance function of the field except for smoothness and isotropy. The results are based on a charact...

Expected Number of Slope Crossings of Certain Gaussian Random Polynomials

Let Qn(x) = ∑n i=0 Aix i be a random 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, assuming A−1 = 0. The coefficients can be considered as n consecutive observations of a Brownian motion. We study the number of times that such a random polynomial cros...

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...