Geodesic
About the number of step functions with restrictions
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 4, pp. 625-651 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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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