  In this paper, we present a new method for the solution of those linear
transport processes that may be described by a Master Equation, such as
electron, neutron and photon transport, and more exotic variants thereof. We
base our algorithm on a Markov process on a Voronoi-Delaunay grid, a
nonperiodic lattice which is derived from a random point process that is chosen
to optimally represent certain properties of the medium through which the
transport occurs. Our grid is locally translation and rotation invariant in the
mean. We illustrate our approach by means of a particular example, in which the
expectation value of the length of a grid line corresponds to the local mean
free path. In this example, the lattice is a direct representation of the `free
path space' of the medium. Subsequently, transport is defined as simply moving
particles from one node to the next, interactions taking place at each point.
We derive the statistical properties of such lattices, describe the limiting
behavior, and show how interactions are incorporated as global coefficients.
Two elementary linear transport problems are discussed: that of free ballistic
transport, and the transport of particles through a scattering medium. We also
mention a combination of these two. We discuss the efficiency of our method,
showing that it is much faster than most other methods, because the operation
count does not scale with the number of sources. (ABRIDGED)
