Quantitative analysis of probabilistic dependencies in a thermal balanced traffic gas

We exploit some fundamental properties of functional convolutions to detect the range of interactions between particles in a one dimensional thermal-relaxed traffic gas. We investigate how much the convolution of the probability distributions describing the inter-particle spacing probabilities diverges from the joint probability of these distributions, and interpret an associate perturbation as a probabilistic dependence of the random variables describing inter-particle spacings. By means of perturbation intensity we derive the number of interacting particles - the interaction range.