Alperen Özdemir: Martingales and descents

Abstract: We show a technique to write Eulerian statistics as sums of martingale differences. This provides a new proof of the fact that the number of descents in random permutations is asymptotically normal and a strong error bound for the convergence. Similar applications will be presented for other descent-related statistics including the number of inversions, descents in Stirling permutations, descents in involutions, descents in derangements, the length of the longest alternating subsequences and two-sided Eulerian numbers.