The size of the connected components of excursion sets of x^2, t and F fields

The distribution of the size of one connected component and the largest connected component of the excursion set is derived for stationary x^2, t and F fields, in the limit of high or low thresholds. This extends previous results for stationary Gaussian fields (Nosko 1969, Adler 1981) and for x^2 fields in one and two dimensions (Aronowich and Adler 1986, 1988). An application of this is to detect regional changes in positron emission tomography (PET) images of blood flow in human brain, using the size of the largest connected component of the excursion set as a test statistic.