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We provide analytical results for the probability distribution of a family ofwavefunctions of a quantum mechanics model of commuting matrices in the large-Nlimit. These wavefunctions describe the strong coupling limit of 1/8 BPS statesof N=4 supersymmetric Yang-Mills theory. Therefore, in the large-N limit, theyshould be dual to classical solutions of type IIB supergravity thatasymptotically approach AdS5xS5. Each probability distribution can be describedas the partition function of a matrix model (different wavefunctions correspondto different matrix model potentials) which we study by means of a saddle pointapproximation. These saddle point solutions are given in terms of(five-dimensional) hypersurfaces supporting density distributions ofeigenvalues.

Shaping up BPS States with Matrix Model Saddle Points