  We examine the contact statistics of noninteracting random walkers on a
two-dimensional plane. We find that the waiting time between successive
contacts for an individual (the interarrival time) is non-exponentially
distributed, with consequent non-Poison distributed contact counts. This
manifests as over-dispersion of the contact-count probability mass function,
caused by negative duration dependence of the waiting time interval when the
walkers are in close proximity. While successive contacts are independent, the
probability of repeat contact between individuals decreases with time after a
previous contact. Further, contact duration depends sensitively on walker
radius. For walker radii smaller than both the mean step length and the mean
nearest neighbor separation, the probability density of the contact duration is
strongly peaked at the ballistic crossing time for head-on collisions. The
contact statistics of individuals in biological populations, dilute components
of chemical systems, or Lagrangian particles in turbulent flows depends
critically on the behavior at close proximity, whether it is attractive,
repulsive, or neutral. This work clarifies those statistics for the neutral
case, under the assumption that the underlying motions approximate a collection
of random walkers, and we suggest it may be useful in understanding contagion
in human populations.
