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.