### Martingales and descents

- Series
- Stochastics Seminar
- Time
- Thursday, March 5, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Alperen Ozdemir – University of Southern California – aozdemir@usc.edu

We provide a martingale proof of the fact that the number of descents in random permutations is asymptotically normal with an error bound of order n^{-1/2}. The same techniques are shown to be applicable to other descent and descent-related statistics as they satisfy certain recurrence relation conditions. These statistics include inversions, descents in signed permutations, descents in Stirling permutations, the length of the longest alternating subsequences, descents in matchings and two-sided Eulerian numbers.