Shaping up BPS states with matrix model saddle points

We provide analytical results for the probability distribution of a family of wavefunctions of a quantum mechanics model of commuting matrices in the large-N limit. These wavefunctions describe the strong coupling limit of 1/8 BPS states of \ {N}=4 supersymmetric Yang-Mills theory. In the large-N limit, they should be dual to classical solutions of type IIB supergravity that asymptotically approach AdS₅ × S⁵. Each probability distribution can be described as the partition function of a matrix model (different wavefunctions correspond to different matrix model potentials) which we study by means of a saddle point approximation. These saddle point solutions are given in terms of (five-dimensional) hypersurfaces supporting density distributions of eigenvalues.