The Limit Shape Problem for Ensembles of Young Diagrams

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Focusing on ensembles of Young diagrams from group theory, this book explores their statistical properties in large-scale limits. It highlights the emergence of specific curves in the scaling limits of Young diagram profiles, linking this to significant studies in harmonic analysis of symmetry structures. The author develops an asymptotic theory for symmetric group representations as n approaches infinity, utilizing rigorous limit theorems and combinatorial analysis. The goal is to provide a comprehensive understanding of the asymptotic behavior of rescaled profiles in the Plancherel ensemble.