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Creators/Authors contains: "Boardman, Samuel"

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  1. ; ; (, Journal of Applied Probability)
    Abstract We study an example of a hit-and-run random walk on the symmetric group $$\mathbf S_n$$ . Our starting point is the well-understood top-to-random shuffle. In the hit-and-run version, at each single step , after picking the point of insertion j uniformly at random in $$\{1,\ldots,n\}$$ , the top card is inserted in the j th position k times in a row, where k is uniform in $$\{0,1,\ldots,j-1\}$$ . The question is, does this accelerate mixing significantly or not? We show that, in $L^2$ and sup-norm, this accelerates mixing at most by a constant factor (independent of n ). Analyzing this problem in total variation is an interesting open question. We show that, in general, hit-and-run random walks on finite groups have non-negative spectrum. 
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