  We study the free energy of a particle in (arbitrary) high-dimensional
Gaussian random potentials with isotropic increments. We prove a computable
saddle-point variational representation in terms of a Parisi-type functional
for the free energy in the infinite-dimensional limit. The proofs are based on
the techniques developed in the course of the rigorous analysis of the
Sherrington-Kirkpatrick model with vector spins.
