Random polynomials
The author studies several interesting differences of the behaviour between the algebraic and trigonometric curves. He shows that the trigonometric curves on an average oscillate more frequently than the algebraic ones and that the number of K level-crossings of the trigonometric curves is the same as for x-axis crossings which for the algebraic case decreases as K increases. He also shows that changing zero mean to a non-zero mean will not affect the number of crossings of trigonometric curves whereas in the case of algebraic curves, it is reduced by half. He also obtains a formula for the expected number of crossings using the Kac-Rice formula.
scientific article; zbMATH DE number 4163854