Moderate deviations for longest increasing subsequences : the lower tail
Matthias Löwe, Franz Merkl, Silke W. W. Rolles · TU/e Research Portal · 2000
We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation.It refers to the regime between the lower tail large deviation regime and the central limit regime.The present article together with the upper tail moderate deviation principle in 12] yields a complete picture for the whole moderate deviation regime.Other than in 12], we can directly apply estimates by Baik, Deift, and Johansson 3], who obtained a (non-standard) Central Limit Theorem for the same quantity.