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 proven in 1999 by Jinho Baik, Percy Deift and Kurt Johansson.

be a uniformly chosen permutation with length

be the length of the longest, increasing subsequence of

is the Tracy-Widom distribution of the Gaussian unitary ensemble.