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.
The theorem was proven in 1999 by Jinho Baik, Percy Deift and Kurt Johansson. [1] [2]
For each let be a uniformly chosen permutation with length . Let be the length of the longest, increasing subsequence of .
Then we have for every that
where is the Tracy-Widom distribution of the Gaussian unitary ensemble.
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.
The theorem was proven in 1999 by Jinho Baik, Percy Deift and Kurt Johansson. [1] [2]
For each let be a uniformly chosen permutation with length . Let be the length of the longest, increasing subsequence of .
Then we have for every that
where is the Tracy-Widom distribution of the Gaussian unitary ensemble.