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A random walk representation of the Dirac propagator |
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| Authors: | Jan Ambj rn Bergfinnur Durhuus Thordur Jonsson |
| Affiliation: | The Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark The Mathematics Institute, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark The Niels Bohr Institute and NORDITA, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark |
| Abstract: | 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. |
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