About the number of step functions with restrictions

R. Ahlswede^a, V. M. Blinovskii<sup>b

a</sup> Bielefeld University
^b Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: 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.

Received: 17.08.2004

DOI: 10.4213/tvp123

 English version: Theory of Probability and its Applications, 2006, 50:4, 537–560

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