We study the limiting distribution of the maximum value of a stationary bivariate real random field satisfying suitable weak mixing conditions. In the first part, when the double dimensions of the random samples have a geometric growing pattern, a max-semistable distribution is obtained. In the second part, considering the random field sampled at double random times, a mixture distribution is established for the limiting distribution of the maximum.
stationary random fields, max-semistable laws, random double sample size
60G60, 60G70