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**Harvard**

Jonasson, J. (2015) *Card-cyclic-to-random shuffling with relabeling*.

** BibTeX **

@article{

Jonasson2015,

author={Jonasson, Johan},

title={Card-cyclic-to-random shuffling with relabeling},

journal={Alea-Latin American Journal of Probability and Mathematical Statistics},

issn={1980-0436},

volume={12},

issue={2},

pages={793-810},

abstract={The card-cyclic-to-random shuffle is the card shuffle where the n cards arc labeled 1,...,n according to their starting positions. Then the cards are mixed by first picking card] from the deck and reinserting it at a uniformly random position, then repeating for card 2, then for card 3 and so on until all cards have been reinserted in this way. Then the procedure starts over again, by first picking the card with label 1 and reinserting, and so on. Morris et al. (2014) recently showed that the order of the number of shuffles needed to mix the deck in this way is n log n. In the present paper, we consider a variant of this shuffle with relabeling, i.e. a shuffle that differs from the above in that after one round, i.e. after all cards have been reinserted once, we relabel the cards according to the positions in the deck that they now have. The relabeling is then repeated after each round of shuffling. It is shown that even in this case, the correct order of mixing is n log n.},

year={2015},

keywords={mixing time, stability of eigenvalues},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 243702

A1 Jonasson, Johan

T1 Card-cyclic-to-random shuffling with relabeling

YR 2015

JF Alea-Latin American Journal of Probability and Mathematical Statistics

SN 1980-0436

VO 12

IS 2

SP 793

OP 810

AB The card-cyclic-to-random shuffle is the card shuffle where the n cards arc labeled 1,...,n according to their starting positions. Then the cards are mixed by first picking card] from the deck and reinserting it at a uniformly random position, then repeating for card 2, then for card 3 and so on until all cards have been reinserted in this way. Then the procedure starts over again, by first picking the card with label 1 and reinserting, and so on. Morris et al. (2014) recently showed that the order of the number of shuffles needed to mix the deck in this way is n log n. In the present paper, we consider a variant of this shuffle with relabeling, i.e. a shuffle that differs from the above in that after one round, i.e. after all cards have been reinserted once, we relabel the cards according to the positions in the deck that they now have. The relabeling is then repeated after each round of shuffling. It is shown that even in this case, the correct order of mixing is n log n.

LA eng

LK http://alea.impa.br/articles/v12/12-30.pdf

OL 30