Hard rods: statistics of parking configurations

Abstract

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

9 pages, 1 figure