The geometry of correlation fields with an application to functional connectivity of the brain (Q1578605)

Let \(X\), \(Y\) be vectors of \(d\) stationary Gaussian random fields, and \[ R(s,t):= {\langle x(s),y(t)\rangle\over \sqrt{\langle x(s), x(s)\rangle\langle y(t), y(t)\rangle}} \] the cross correlation. The authors present statistically interesting and important results on the excursion set of \(R\) over a threshold level and also on the maximal component of the excursion set. Simulations and applications in brain research are given.