University of Cambridge > Talks.cam > Probability > Lengths of Monotone Subsequences in a Mallows Permutation

Lengths of Monotone Subsequences in a Mallows Permutation

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact jrn10.

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 2sqrt(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 q^Inv(p) where q is a real parameter and Inv(p) is the number of inversions in p. We determine the typical order of magnitude of the LIS and LDS , large deviation bounds for these lengths and a law of large numbers for the LIS for various regimes of the parameter q.

This is joint work with Ron Peled.

This talk is part of the Probability series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity