Finite size corrections relating to distributions of the length of longest increasing subsequences

Abstract

Considered are the large N, or large intensity, forms of the distribution of the length of the longest increasing subsequences for various models. Earlier work has established that for finite N or finite intensity these distributions relate to certain hard edge distribution functions in random matrix theory, with the limit laws corresponding to a hard to soft edge transition. By analysing this transition, we supplement and extend results of Baik and Jenkins for the Hammersley model and symmetrisations, which give that the leading correction is proportional to z−2/3, where z2 is the intensity of the Poisson rate, and provide a functional form of the leading correction. Our methods give the fu..