Hard rods: statistics of parking configurations

Abstract

We compute the correlation function in the equilibrium version of R\'enyi's {\sl parking problem}. The correlation length is found to diverge as $2^{-1}\pi^{-2}(1-\rho)^{-2}$ when $\rho\nearrow1$ (maximum density) and as $\pi^{-2}(2\rho-1)^{-2}$ when $\rho\searrow1/2$ (minimum density).