Expected Number of Local Maxima of Some Gaussian Random Polynomials

Expected Number of Local Maxima of Some Gaussian Random Polnomials

On the average number of sharp crossings of certain Gaussian random polynomials

Local Maxima and the Expected Euler Characteristic of Excursion Sets of 2 , F and T Elds

SUMMARY The maximum of a Gaussian random eld was used by Worsley et al. (1992) to test for activation at an unknown point in positron emission tomography images of blood ow in the human brain. The Euler characteristic of excursion sets was used as an estimator of the number of regions of activation. The expected Euler characteristic of excursion sets of stationary Gaussian random elds has been ...

Local maxima and the expected Euler characteristic of excursion sets of χ, F and t fields

The maximum of a Gaussian random field was used by Worsley et al. (1992) to test for activation at an unknown point in positron emission tomography images of blood flow in the human brain. The Euler characteristic of excursion sets was used as an estimator of the number of regions of activation. The expected Euler characteristic of excursion sets of stationary Gaussian random fields has been de...

On Classifications of Random Polynomials

 Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+...