wigner_semi_circle.m

%% copy from ocw.mit.edu
%% random matrix theory

%n=20; s=30000; d=.05; %matrix size, samples, sample dist
n=10; s=1000; d=.05; % s=30000 is too slow
e=[]; %gather up eigenvalues
im=1; %imaginary(1) or real(0)

for i=1:s,
  a=randn(n)+im*sqrt(-1)*randn(n);a=(a+a')/(2*sqrt(2*n*(im+1)));
  v=eig(a)'; e=[e v];
end

hold off; [m x]=hist(e,-1.5:d:1.5); bar(x,m*pi/(2*d*n*s));
axis('square'); axis([-1.5 1.5 -1 2]); hold on;
t=-1:.01:1; plot(t,sqrt(1-t.^2),'r');