  This paper presents a simple model that mimics quantum mechanics (QM) results
in terms of probability fields of free particles subject to self-interference,
without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM
picture, the proposed model only uses integer-valued quantities and arithmetic
operations. In particular, it assumes a discrete spacetime under the form of an
euclidean lattice. The proposed approach describes individual particle
trajectories as random walks. Transition probabilities are simple functions of
a few quantities that are either randomly associated to the particles during
their preparation, or stored in the lattice sites they visit during the walk.
Non-relativistic QM predictions, particularly self-interference, are retrieved
as probability distributions of similarly-prepared ensembles of particles.
Extension to interacting particles is discussed but not detailed in this paper.
