Aznar Martínez, M Bruno (0005) Asymptotic Convergence of Young Diagrams under the Plancherel Measure PRE - Research Project, ENSTA.



We revisit a well-known combinatorial analysis result found independently by Logan and Shepp, and Vershik and Kerov in 1977: the asymptotic convergence in probability of Young diagrams under the Plancherel measure to a certain function called limit shape. Neither of the authors nor any subsequent published article we have come across provides with the method-ology to compute said limit form. After an overview of the underlying linear representation theory behind the problem, we set ourselves to come up with the formula of the limit shape, introducing the notion of energy-entropy functionals for the upper border function of diagrams. We then relate them to a Riemann-Hilbert problem through a variational approach, which lead us to consider hypergeometric functions right before the internship ended in an inconclusive manner.

Item Type:Thesis (PRE - Research Project)
Subjects:Mathematics and Applications
ID Code:8398
Deposited By:bruno Aznar martinez
Deposited On:19 août 2021 10:04
Dernière modification:19 août 2021 10:04

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