Nov. 22, 3:30pm, Wean 8220 (Note unusual day)

Nayantara Bhatnagar, University of Delaware

Lengths of Monotone Subsequences in a Mallows Permutation

Nayantara Bhatnagar, University of Delaware

Lengths of Monotone Subsequences in a Mallows Permutation

Abstract:

The longest increasing subsequence (LIS) of a uniformly random permutation is a well studied problem. Vershik–Kerov and Logan–Shepp first showed that asymptotically the typical
length of the LIS is 2√n . This line of research culminated in the work of Baik–Deift–Johansson who related this length to the Tracy–Widom distribution.

We study the length of the LIS and LDS of random permutations drawn from the Mallows measure, introduced by Mallows in connection with ranking problems in statistics. Under this
measure, the probability of a permutation *p* in *S _{n}* is proportional to

This is joint work with Ron Peled.