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A weak law of large numbers for the lengths of longest increasing subsequences in Mallows random permutations
Probability| Speaker: | Shannon Starr, University of Rochester |
| Location: | 1147 MSB |
| Start time: | Wed, Mar 10 2010, 4:10PM |
Description
Mallows random permutations are random permutations with a
slightly different probability measure than the uniform Haar measure.
By choosing the parameters appropriately, however, one can choose the
Mallows measures to be asymptotically absolutely continuous with
respect to the uniform measures in a certain sense. We use the well
known theorem of Vershik and Kerov, and Logan and Shepp, which gives a
law of large numbers for the lengths of the longest increasing
subsequences for uniform random permutations, to prove an analogous
result for Mallows random permutations. The interesting problem of
describing fluctuations is open (and was posed by Borodin, Diaconis
and Fulman in a recent paper). This talk is based on joint work with
Carl Mueller.