Geodesic
About the number of step functions with restrictions
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 4, pp. 625-651

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We obtain an asymptotic formula for the number of scaled step functions with restrictions on the length and height of steps (shapes of Young diagrams) of a given area in the neighborhood of a given curve. This allows us to find the asymptotics of the whole number of such functions and find the limit shape — the curve of concentration of the step functions.
Keywords: large deviations, random walk, Young diagram. 
R. Ahlswede; V. M. Blinovskii. About the number of step functions with restrictions. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 4, pp. 625-651. http://geodesic.mathdoc.fr/item/TVP_2005_50_4_a0/
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[1] Vershik A. M., “Statisticheskaya mekhanika kombinatornykh razbienii i ikh predelnye konfiguratsii”, Funkts. analiz i ego pril., 30:2 (1996), 19–39 | MR | Zbl

[2] Chandrasekkharan K., Arifmeticheskie funktsii, Nauka, M., 1975, 272 pp. | MR

[3] Blinovskii V. M., “Printsip bolshikh uklonenii dlya granitsy sluchainoi diagrammy Yunga”, Problemy peredachi informatsii, 35:1 (1999), 61–74 | MR

[4] Blinovsky V. M., “Large deviations problem for the shape of a random Young diagram with restrictions”, Numbers, Information and Complexity, eds. I. Althöfer et al., Kluwer, Dordrecht, 2000, 473–488 | MR | Zbl

[5] Dembo A., Vershik A., Zeitouni O., “Large deviations for integer partitions”, Markov Process. Related Fields, 6:2 (2000), 147–179 | MR | Zbl

[6] Dembo A., Zeitouni O., Large Deviations Techniques and Applications, Jones and Bartlett, Boston, 1993, 346 pp. | MR | Zbl

[7] Gelfand I. M., Fomin S. V., Variatsionnoe ischislenie, Fizmatgiz, M., 1961, 228 pp. | MR

[8] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, v. 2, Mera, integral Lebega, gilbertovo prostranstvo, Izd-vo Mosk. un-ta, M., 1960, 118 pp. | MR