Abstract
A family of m independent identically distributed random variables indexed by a chemical potential φ∈[0,γ] represents piles of particles. As φ increases to γ, the mean number of particles per site converges to a maximal density ρ c <∞. 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.
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Ferrari, P.A., Landim, C. & Sisko, V.V. Condensation for a Fixed Number of Independent Random Variables. J Stat Phys 128, 1153–1158 (2007). https://doi.org/10.1007/s10955-007-9356-3
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DOI: https://doi.org/10.1007/s10955-007-9356-3