Geodesic
Limits shapes of Young diagrams. Two elementary approaches
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 40, Tome 370 (2009), pp. 111-131

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We present a techniques for obtaining the limit shapes of Yong diagrams with respect to multiplicative measures, which arise in statistical mechanics. Our approach does not use neither complex analysis, nor Tauberian theorems. Also, we get the limit shape for bounded and unbounded partitions with respect to uniform measure, avoiding even generating functions. Bibl. – 6 titles. 
@article{ZNSL_2009_370_a6,
     author = {F. Petrov},
     title = {Limits shapes of {Young} diagrams. {Two} elementary approaches},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {111--131},
     publisher = {mathdoc},
     volume = {370},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_370_a6/}
}
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F. Petrov. Limits shapes of Young diagrams. Two elementary approaches. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 40, Tome 370 (2009), pp. 111-131. http://geodesic.mathdoc.fr/item/ZNSL_2009_370_a6/