First example is correct. Second one is reducible i think

@CarloBeenakker My bad! I got confused. Its not Ginibre ensemble. But the joint distribution is correct i.e. $$P_{N,K}(\vec{\lambda})=\delta\left(1-\sum_{j=1}^N\lambda_j\right)\prod_i\lambda_i^{K-N}\prod_{i<j}(\lambda_i-\lambda_j)^2$$ I'm going through this. Pg2