Journal of Applied Probability | VOL. 59

# The hit-and-run version of top-to-random

Publication Date Jul 12, 2022

## Abstract

AbstractWe 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 jth 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.

## ConceptsPowered By Our platform integrates UNSILO’s semantic concept extraction, with power of ML, to identify the most relevant papers for you.

Top Card Non-negative Spectrum Random Walk Symmetric Group Constant Factor Total Variation Finite Groups Single Step Problem In Variation Point Of Insertion

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