Limit theorems are proved for fixed points, descents, and inversions under iterated random-to-top shuffles, with new combinatorial proofs resolving open questions on expectations.
Ross,Fundamentals of stein’s method, Probability Surveys8(2011), 210–293
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On the statistics of random-to-top shuffles
Limit theorems are proved for fixed points, descents, and inversions under iterated random-to-top shuffles, with new combinatorial proofs resolving open questions on expectations.