Let $(X_j)$ be a real Gaussian stationary sequence, that is, a random sequence whose finite marginals have centered multi-variate Gaussian distribution, and E(X_j X_i) = r(j-i). Given the covariance function r(j), what is the behavior of the probability that X_1>0, X_2>0, ... , X_N>0 as N grows to infinity? This simple question goes back at least to the 1950's, when researchers such as...