I think that the following code is missing a factor of 2 dividing when the function returns.
function rand(d::Wigner{2}, n::Int)
A = randn(n, n) + im*randn(n, n)
normalization = √(4*n)
return Hermitian((A + A') / normalization)
end
That is, replace this line return Hermitian((A + A') / normalization) with this other one return Hermitian( (A + A') / 2 / normalization ).
Thanks and regards
Pablo