Abstract: For a permutation s in S_n, the longest increasing subsequence (LIS) is a subsequence of entries of s whose indices and values are both strictly increasing and whose length is maximal among all such subsequences. In this talk, I will outline a Poissonization method that already captures the first-order behaviour of the LIS length for a uniformly random permutation in S_n. I will then describe the Baik--Deift--Johansson theorem, which identifies the centred and rescaled fluctuations of the LIS length with the Tracy--Widom GUE distribution. I will conclude with a brief indication of how this result fits into the broader Airy_2 universality class.
Longest Increasing Subsequences and the Airy_2 Universality Class
12.12.2025 14:00 - 15:30
Organiser:
A. Carrance, M. Reibnegger
Location:
BZ 6, 6th floor, OMP1