Extremes of independent Gaussian processes

For every n aaEuro parts per thousand acenter dot, let X (1n) ,..., X (nn) be independent copies of a zero-mean Gaussian process X (n) = {X (n) (t), t aaEuro parts per thousand T}. We describe all processes which can be obtained as limits, as n -> aEuro parts per thousand a, of the process a (n) (M (n) -aEuro parts per thousand b (n) ), where M (n) (t) = max (i = 1,...,n) X (in) (t), and a (n) , b (n) are normalizing constants. We also provide an analogous characterization for the limits of the process a (n) L (n) , where L (n) (t) = min (i = 1,...,n) |X (in) (t)|.