Random process theory: probability distribution of height vs summits

Question

Imagine I have a matrix of height values ($z$), e.g. a surface height topography. This surface is a random process: randomly rough isotropic surface with Gaussian distribution.

What is the difference (if there is any difference) between probability distribution of height and probability distribution of summits.

Summits in $z$ are for example defined to be the maximum value of each column of the matrix, i.e. :

[n , m] = size(z)
summit = zeros(m);
for i = 1 : m
    summit(i) = max(z(:,i));
end

If not so complex up to here, I add some more concerns: My real question is, if my original topography is a fractal surface, will the summit profile be a fractal profile with the same scaling behavior?

Thanks!