  We investigate the probability distribution function of the free flight time
and of the number of collisions in a hard sphere gas at equilibrium. At
variance with naive expectation, the latter quantity does not follow Poissonian
statistics, even in the dilute limit which is the focus of the present
analysis. The corresponding deviations are addressed both numerically and
analytically. In writing an equation for the generating function of the
cumulants of the number of collisions, we came across a perfect mapping between
our problem and a previously introduced model: the probabilistic ballistic
annihilation process [Coppex et al., Phys. Rev. E 69 11303 (2004)]. We exploit
this analogy to construct a Monte-Carlo like algorithm able to investigate the
asymptotically large time behavior of the collisional statistics within a
reasonable computational time. In addition, our predictions are confronted
against the results of Molecular Dynamics simulations and Direct Simulation
Monte Carlo technique. An excellent agreement is reported.
