  A new method to perform numerical simulations of light-front Hamiltonians
formulated on transverse lattices is introduced. The method is based on a DLCQ
formulation for the (continuous) longitudinal directions. The hopping term in
the transverse direction introduces couplings between fields defined on
neighboring $1+1$-dimensional sheets. Within each sheet, the light-cone
imaginary time evolution operator is calculated numerically with high precision
using DLCQ. The coupling between neighboring sheets is taken into account using
an initial value random walk algorithm based on the ensemble projector Monte
Carlo technique and a checkerboard decomposition for the time evolution
operator. The structure functions of $\lambda \phi^4$ theory in $2+1$
dimensions are studied as a trial application. The calculations are performed
with up to 64 transverse lattice sites. No Tamm-Dancoff truncations are
necessary.
