Asymptotic expansions relating to the distribution of the length of longest increasing subsequences
Folkmar Bornemann
Abstract:We study the distribution of the length of longest increasing subsequences in random permutations of n integers as n grows large and establish an asymptotic expansion in powers of
$n^{-1/3}$
. Whilst the limit law was already shown by Baik, Deift and Johansson to be the GUE Tracy–Widom distribution F, we find explicit analytic expressions of the first few finite-size correction terms as linear combinations of higher order derivatives of F with rational polynomial coefficients. Our … Show more
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