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Alperen Özdemir: Martingales and descents

Speaker: Alperen Özdemir (KTH)

Time: Wed 2024-09-25 10.15 - 11.15

Location: 3418

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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.