Before revision:  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 .
After revision:  This leads to a negative duration dependence of the waiting-time interval and over dispersion of the contact-count probability density function for all time intervals. The results presented are most relevant to systems in which particle proximity is critical and contact results in no change (or a low probability of change) in the particles' motions, or to systems in which multiple contact encounters are required before interaction .