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Random Walks On Finite Groups With Few Random Generators


 
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1. Title Title of document Random Walks On Finite Groups With Few Random Generators
 
2. Creator Author's name, affiliation, country Igor Pak; Yale University
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Random random walks on groups, random subproducts, probabilistic method, separation distance
 
3. Subject Subject classification Primary 60C05, Secondary 60J15.
 
4. Description Abstract Let $G$ be a finite group. Choose a set $S$ of size $k$ uniformly from $G$ and consider a lazy random walk on the corresponding Cayley graph. We show that for almost all choices of $S$ given $k = 2a\, \log_2 |G|$, $a>1$, this walk mixes in under $m = 2a \,\log\frac{a}{a-1} \log |G|$ steps. A similar result was obtained earlier by Alon and Roichman and also by Dou and Hildebrand using a different techniques. We also prove that when sets are of size $k = \log_2 |G| + O(\log \log |G|)$, $m = O(\log^3 |G|)$ steps suffice for mixing of the corresponding symmetric lazy random walk. Finally, when $G$ is abelian we obtain better bounds in both cases.
 
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7. Date (YYYY-MM-DD) 1998-11-11
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/38
 
10. Identifier Digital Object Identifier 10.1214/EJP.v4-38
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 4
 
12. Language English=en en
 
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