Fragmenting Random Permutations
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چکیده
Problem 1.5.7 from Pitman’s Saint-Flour lecture notes [11]: Does there exist for each n a fragmentation process (Πn,k, 1 ≤ k ≤ n) such that Πn,k is distributed like the partition generated by cycles of a uniform random permutation of {1, 2, . . . , n} conditioned to have k cycles? We show that the answer is yes. We also give a partial extension to general exchangeable Gibbs partitions.
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تاریخ انتشار 2007