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 
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/
@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},
     year = {2009},
     volume = {370},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_370_a6/}
}
TY  - JOUR
AU  - F. Petrov
TI  - Limits shapes of Young diagrams. Two elementary approaches
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 111
EP  - 131
VL  - 370
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_370_a6/
LA  - ru
ID  - ZNSL_2009_370_a6
ER  - 
%0 Journal Article
%A F. Petrov
%T Limits shapes of Young diagrams. Two elementary approaches
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 111-131
%V 370
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_370_a6/
%G ru
%F ZNSL_2009_370_a6

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] A. M. Vershik, S. V. Kerov, “Asimptotika maksimalnoi i tipichnoi razmernostei neprivodimykh predstavlenii simmetricheskoi gruppy”, Funkts. analiz i ego pril., 19:1 (1985), 25–36 | MR | Zbl

[2] M. Szalay, P. Turan, “On some problems of the statistical theory of partitions with application to characters of the symmetric group, I”, Acta Math. Acad. Sci. Hungar, 29:3 (1977), 361–379 | DOI | MR | Zbl

[3] H. N. V. Temperley, “Statistical mechanics and partitions of number, II”, Proc. Cambridge. Philos. Soc., 48 (1952), 683–697 | DOI | MR

[4] A. M. Vershik, “Statisticheskaya mekhanika kombinatornykh razbienii i ikh predelnye konfiguratsii”, Funkts. analiz i ego pril., 30:2 (1996), 19–39 | DOI | MR | Zbl

[5] A. M. Vershik, Yu. V. Yakubovich, “Asimptotika ravnomernoi mery na simpleksakh, sluchainye kompozitsii i razbieniya”, Funkts. analiz i ego pril., 37:4 (2003), 39–48 | DOI | MR | Zbl

[6] A. Vershik, Yu. Yakubovich, “Limit shape and fluctuations of random partitions of naturals with fixed number of summands”, Moscow Math. J., 1:3 (2001), 457–468 | MR | Zbl