function A = randwalk_cube(n)
% the Markov transition matrix

A = zeros(2^n);
for xi = 1:2^n
  x = i2c(xi,2,n);
  A(xi,xi) = 1/2; % stay put w/prob 1/2
  for i=1:n
    y = x;
    y(i) = 1-y(i);
    yi = c2i(y,2,n);
    A(yi,xi) = 1/(2*n); % go to neighbor w/prob 1/(2n)
  end
end

return

function i=c2i(c,m,n)
dims = repmat(m,[1 n]);
i = coord2ind(c+1,dims);
return

function c=i2c(i,m,n)
dims = repmat(m,[1 n]);
c = ind2coord(i,dims)-1;
return