Geodesic
A statistical sum associated with Young diagrams
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part IX, Tome 164 (1987), pp. 20-29

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Asymptotic properties of the sums of powers of normalized dimensions of all irreducible complex representations of the symmetric group $S_N$ as $N\to\infty$ are studied. The limiting Gibbs measure on the space of Young diagrams is calculated. Our approach is related to a special one-dimensional many particles model. In the appendix written by A.M. Pass some numerical and graphic information on the “Helmholtz energy” for the model is presentede Bibl. – 10. 
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     author = {A. M. Vershik},
     title = {A statistical sum associated with {Young} diagrams},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     volume = {164},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_164_a2/}
}
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A. M. Vershik. A statistical sum associated with Young diagrams. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part IX, Tome 164 (1987), pp. 20-29. http://geodesic.mathdoc.fr/item/ZNSL_1987_164_a2/