# Cutoff Phenomenon and Limiting Profile of a Random Walk on the Symmetric Group

@inproceedings{Farah2021CutoffPA, title={Cutoff Phenomenon and Limiting Profile of a Random Walk on the Symmetric Group}, author={A. Farah}, year={2021} }

When shuffling a deck of cards, we’re often interested in in knowing the number of shuffles after which the deck is “sufficiently shuffled,” i.e. given a known starting configuration of the card deck and some probabilistic shuffling algorithm, how many times should we shuffle the deck so that the probability of any card being in any position is (almost) exactly the same? We will consider this basic shuffling algorithm: Using a deck of n cards, laid out and facing down, pick a card A uniformly…

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