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Gibbs Ensembles of Partitions: from limit shapes to hydrodynamic limits

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DNM - The mathematical design of new materials

Distributions of aggregate sizes in various polymerization processes may be described by measures on partitions of integers and sets. We explicitly compute limit shapes for several grand canonical Gibbs ensembles and prove that all possible limit shapes for these ensembles fall into distinct classes determined by the asymptotics of the internal energies of aggregates. Further on, we establish hydrodynamic limits for a class of stochastic processes on the associated Young diagrams and deriving PDEs governing the evolution of limit shapes in suitable asymptotic regimes.




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