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A note on various holding probabilities for random lazy random walks on finite groups

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  • Hildebrand, Martin

Abstract

The author previously considered certain lazy random walks on arbitrary finite groups. Given a k-tuple (g1,...,gk) of elements of a finite group, one multiplies the previous position of the walk by gi[var epsilon] where i is uniform on {1,...,k} and [var epsilon] has a given distribution on {1,0,-1}. The previous work gave good bounds if P([var epsilon]=1)=P([var epsilon]=-1)=1/4 and P([var epsilon]=0)=1/2 or if P([var epsilon]=1)=P([var epsilon]=0)=1/2. The current paper develops some elementary comparison techniques which work for other distributions for [var epsilon] such as P([var epsilon]=1)=P([var epsilon]=0)=P([var epsilon]=-1)=1/3.

Suggested Citation

  • Hildebrand, Martin, 2002. "A note on various holding probabilities for random lazy random walks on finite groups," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 199-206, January.
  • Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:199-206
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