Market›Baik–Deift–Johansson theorem
Company Profile

Baik–Deift–Johansson theorem

The Baik–Deift–Johansson theorem is a result from probabilistic combinatorics. It deals with the subsequences of a randomly uniformly drawn permutation from the set . The theorem makes a statement about the distribution of the length of the longest increasing subsequence in the limit. The theorem was influential in probability theory since it connected the KPZ-universality with the theory of random matrices.

Statement
For each N \geq 1 let \pi_N be a uniformly chosen permutation with length N. Let l(\pi_N) be the length of the longest, increasing subsequence of \pi_N. Then we have for every x \in \mathbb{R} that :\mathbb{P}\left(\frac{l(\pi_N)-2\sqrt{N}}{N^{1/6}}\leq x \right)\to F_2(x),\quad N \to \infty where F_2(x) is the Tracy-Widom distribution of the Gaussian unitary ensemble. == Literature ==
Source: Wikipedia ↗
tickerdossier.comtickerdossier.substack.com