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Partial shuffles by lazy swaps

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  • UserRobert Johnstone (QMUL)
  • ClockThursday 04 May 2023, 14:30-15:30
  • HouseMR12.

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Suppose we generate a random permutation using a sequence of random swaps—that is, we perform a sequence of moves each of which involves swapping a pair of elements in given positions with given probability.

How many such moves are needed to make sure that at the end we have a uniformly random permutation? What if we just require that every element is equally likely to be in any position? And what if we insist that every pair, or just a single fixed pair, of elements is uniformly distributed?

I will discuss some problems and results on these questions and related ones.

Joint work with Barnabás Janzer and Imre Leader.

This talk is part of the Combinatorics Seminar series.

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