  A formula is derived that relates the ground-state dispersion of a many-body
system with the end-to-end distribution of paths with open boundary conditions
in imaginary time. The formula does not involve the energy estimator. It allows
direct measurement of the ground-state dispersion by quantum Monte Carlo
methods without analytical continuation or auxiliary fitting. The formula is
applied to the lattice polaron problem. The exact polaron spectrum and density
of states are calculated for several models in one, two, and three dimensions.
In the adiabatic regime of the Holstein model, the polaron density of states
deviates spectacularly from the free-particle shape.
