%% The distribution of the top eigenvalue

RUNS = 1000;

figure; hold on;

Ns = [10, 50, 100];

for N = Ns
    topEig = zeros(1,RUNS);
    for j = 1:RUNS
        topEig(j) = max(eig(GOE(N)));
    end;

    histogram(topEig, 'Normalization', 'pdf');
end;

legend(num2str(Ns(1)), num2str(Ns(2)), num2str(Ns(3)));