The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd p. We establish the…

We extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be interpreted as a quantified version of the law of large numbers for  positive semi-definite matrices which…