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

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  • Hildebrand, Martin
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 56 (2002)
    Issue (Month): 2 (January)
    Pages: 199-206

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    Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:199-206

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