Geodesic
Numerical data on the typical dimensions of irreducible sepresentations of symmetric groups
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part V, Tome 123 (1983), pp. 152-154

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We give numerical evidence in favour of hypothesis on the asympotic probabilities equidistribution of the typical representations of symmetric groups. An estimate for the entropy of the limiting Plancherel measure is presented. 
@article{ZNSL_1983_123_a10,
     author = {A. M. Vershik and A. B. Gribov and S. V. Kerov},
     title = {Numerical data on the typical dimensions of irreducible sepresentations of symmetric groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {152--154},
     publisher = {mathdoc},
     volume = {123},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_123_a10/}
}
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A. M. Vershik; A. B. Gribov; S. V. Kerov. Numerical data on the typical dimensions of irreducible sepresentations of symmetric groups. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part V, Tome 123 (1983), pp. 152-154. http://geodesic.mathdoc.fr/item/ZNSL_1983_123_a10/