Classical diffusion of N interacting particles in one dimension: General results and asymptotic laws

I consider the coupled one-dimensional diffusion of a cluster of N classical particles with contact repulsion. General expressions are given for the probability distributions, allowing to obtain the transport coefficients. In the limit of large N , and within a Gaussian approximation, the diffusion constant is found to behave as N −1 for the central particle and as (ln N ) −1 for the edge ones. Absolute correlations between the edge particles increase as (ln N ) 2 . The asymptotic one-body distribution is obtained and discussed in relation of the statistics of extreme events.