A random walk representation of the Dirac propagator

We define a discrete random walk with a matrix valued transition function and show that the scaling limit of the two point function of the walk is given by the Dirac propagator. We study the scaling limit of similar walks with curvature dependent transition functions, which are analogous to the Ornstein-Uhlenbeck process, and show that the Dirac propagator can be recovered by a limiting procedure. (orig.)