  We examine a very simple conceptual model of stochastic behavior based on a
random walk process in velocity space. For objects engaged in classical
non-relativistic velocities, this leads under asymmetric conditions to
acceleration processes that resemble the behavior of objects subject to
Newton's second law, and in three dimensional space, acceleration dependent on
an inverse square law emerges. Thus, a non-relativistic random walk would
appear to be capable of describing certain prominent features of classical
physics; however, this classical behavior appears to be able to take place only
for objects with mass exceeding a threshold value which we identify with the
Planck mass. Under these circumstances, stochastic space-time displacements
would be smaller than the Planck length and the Planck time so that such
classically behaved objects would be effectively localized. Lower mass objects
exhibit more rapid diffusion and less localization, and a relativistic random
walk would seem to be required of objects having masses comparable to and
smaller than the threshold mass value. Results suggest the possibility of an
intrinsic quantum-classical transition in the microgram mass range.
