The Size of the Connected Components of Excursion Sets of x, sup 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 sup 2, t and F fields, in the limit of high or low thresholds. This extends previous result for stationary Gaussian fields (Nosko, 1969; Adler, 1981) and for X sup 2 fields in one and two dimensions (Aronowich and Adler, 1986, 1988). An application of this is to detect regional changes in position emission tomography images of blood flow in human brain, using the size of the largest connected component of the excursion set as a test statistic