Condensation for a Fixed Number of Independent Random Variables |
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Authors: | Pablo A Ferrari Claudio Landim Valentin V Sisko |
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Institution: | 1.IME USP,Sao Paulo,Brazil;2.IMPA,Rio de Janeiro,Brazil;3.CNRS UMR 6085,Université de Rouen, UMR 6085,Saint-Etienne-du-Rouvray,France |
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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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Keywords: | Condensation Critical density |
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