  A bounded random walk exhibits strong correlations between collisions with a
boundary. For an one-dimensional walk, we obtain the full statistical
distribution of the number of such collisions in a time t. In the large t
limit, the fluctuations in the number of collisions are found to be
size-independent (independent of the distance between boundaries). This occurs
for any inter-boundary distance, including less and greater than the
mean-free-path, and means that this boundary effect does not decay with
increasing system-size. As an application, we consider spin-polarized gases,
such as 3-Helium, in the three-dimensional diffusive regime. The above results
mean that the depolarizing effect of rare magnetic-impurities in the container
walls is orders of magnitude larger than a Smoluchowski assumption (to neglect
correlations) would imply. This could explain why depolarization is so
sensitive to the container's treatment with magnetic fields prior to its use.

Atomic Physics;Statistical Mechanics