On the intervals between successive zeros of a random function
Michael Selwyn Longuet-Higgins · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1958
Abstract A new approach is suggested to the problem of the statistical distribution of the intervals between successive zeros of a random, Gaussian function. Hence is derived a sequence of approximations pn(r) (n = 3, 4, 5, ...) to the desired probability density p(r). The third approximation p3 is already correct to order r4, and has the correct limiting form in the case of a narrow spectrum. The analysis also gives rise to an alternative approximation p*n(r), less accurate for small values of r, but possibly more accurate for larger values. Numerical computation of both p3, p4, p5 and p*3, p*4, p*5 is carried out for a low-pass spectrum, and the results are compared with observation.