Condensation for a fixed number of independent random variables

Abstract

A family of m independent identically distributed random variables indexed by a chemical potential ϕ\in[0,γ] represents piles of particles. As ϕincreases to γ, the mean number of particles per site converges to a maximal density ρ_c<\infty. The distribution of particles conditioned on the total number of particles equal to n does not depend on ϕ(canonical ensemble). For fixed m, as n goes to infinity the canonical ensemble measure behave as follows: removing the site with the maximal number of particles, the distribution of particles in the remaining sites converges to the grand canonical measure with density ρ_c; the remaining particles concentrate (condensate) on a single site.