Abstract: In the study of matrix models with an AB interaction, that is with Hamiltonian $N tr (V(A_N)+V(B_N)+\lambda A_NB_N)$, a special role is played by spherical integrals of the form $$ \int_{U_N,O_N}\exp (-N tr A_N U_N B_N U_N^*)d\mu(U_N) $$ where the integration is with respect to the Haar measure. I will describe joint work with A. Guionnet, where exponential asymptotics (in the scale $N^2$) for spherical integrals are obtained, based on the stochastic calculus approach developped by Cabanal-Duvillard and Guionnet. The approach does not use Itzykson-Zuber formulae. I will also review some implications for matrix models.