Before revision:  We examine the contact statistics of noninteracting random walkers on a two-dimensional plane  .
After revision:  We examine the contact statistics of noninteracting random walkers on a two-dimensional plane , as a function of the population number density, walker radius, and random-walk step size. The mean-free-collision and the ballistic-crossing times are key parameters. The contact-interval is exponentially distributed for times longer than the mean-free-collision time but not for times shorter than that, and the contact duration distribution is strongly peak at the ballistic-crossing time for head-on collisions, when the ballistic-crossing time is short compared to the mean step duration .