A central limit theorem for two-sided descents of Mallows permutations

Seminar | February 12 | 3:10-4 p.m. | 330 Evans Hall

 Jimmy He, Stanford University

 Department of Statistics

The Mallows measure on the symmetric group gives a way to generate random permutations which are more likely to be sorted than not. There has been a lot of recent work to try and understand limiting properties of Mallows permutations. I'll present work in progress on a central limit theorem for two-sided descents, a statistic counting the number of "drops" in a permutation and its inverse, generalizing work of Chatterjee and Diaconis, and Vatutin. The proof is new even in the uniform case and uses Stein's method with a size-bias coupling.