  Stable laws can be tempered by modifying the L\'evy measure to cool the
probability of large jumps. Tempered stable laws retain their signature power
law behavior at infinity, and infinite divisibility. This paper develops random
walk models that converge to a tempered stable law under a triangular array
scheme. Since tempered stable laws and processes are useful in statistical
physics, these random walk models can provide a basic physical model for the
underlying physical phenomena.
