Nonabelian Localization for Statistical Mechanics of Matrix Models at High Temperatures

We show that in the high temperature limit the partition function of a matrix model is localized on certain shells in the phase space where on each shell the classically conjugate matrix variables obey the canonical commutation relations. The result is obtained by applying the nonabelian equivariant localization principle to the partition function of a matrix model driven by a specific random external source coupled to a conserved charge of the system.