Sum of large random matrices — eigenvalue distribution converges to free convolution of semicircles
N = 60
Eigenvalue range: —
Predicted radius: —
Free convolution: For two independent GUE matrices A, B with semicircular distributions of radii rA, rB, A+B has semicircle of radius √(rA²+rB²). This is the free analogue of classical convolution where variances add. The empirical eigenvalue histogram converges to this as N→∞.