Alperen Özdemir: Martingales and combinatorial statistics

Abstract: We give a martingale proof that the number of descents in a random permutation is asymptotically normal, along with a bound of optimal order on the error of the normal approximation. The same technique applies to a class of combinatorial statistics satisfying certain recurrence relations, including inversions, descents in Stirling permutations, the length of the longest alternating subsequence, descents in matchings, two-sided Eulerian numbers and bivariate peak counts.