NDLI: Random Walks on Dihedral Groups

Content Provider	Springer Nature Link
Author	McCollum, Joseph
Copyright Year	2010
Abstract	In this paper, we look at the lower bounds of two specific random walks on the dihedral group. The first theorem discusses a random walk generated with equal probabilities by one rotation and one flip. We show that roughly p $^{2}$ steps are necessary for the walk to become close to uniformly distributed on all of D $_{2p }$ where p≥3 is an integer. Next we take a random walk on the dihedral group generated by a random k-subset of the dihedral group. The latter theorem shows that it is necessary to take roughly p $^{2/(k−1)}$ steps in the typical random walk to become close to uniformly distributed on all of D $_{2p }$. We note that there is at least one rotation and one flip in the k-subset, or the random walk generated by this subset has periodicity problems or will not generate all of D $_{2p }$.
Ending Page	408
Page Count	12
Starting Page	397
File Format	PDF
ISSN	08949840
e-ISSN	15729230
Journal	Journal of Theoretical Probability
Issue Number	2
Volume Number	24
Language	English
Publisher	Springer US
Publisher Date	2010-09-10
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lower bounds Random walk Probability Theory and Stochastic Processes Statistics Sums of independent random variables; random walks Dihedral group
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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Random Walks on Dihedral Groups