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April 1996 Enumeration and random random walks on finite groups
Carl Dou, Martin Hildebrand
Ann. Probab. 24(2): 987-1000 (April 1996). DOI: 10.1214/aop/1039639374


This paper examines random walks on a finite group G and finds upper bounds on how long it takes typical random walks supported on $(\log|G|)^a$ elements to get close to uniformly distributed on G. For certain groups, a cutoff phenomenon is shown to exist for these typical random walks. A variation of the upper bound lemma of Diaconis and Shahshahani and some counting arguments related to a group equation are used to get the upper bound. A further example which uses this variation is discussed.


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Carl Dou. Martin Hildebrand. "Enumeration and random random walks on finite groups." Ann. Probab. 24 (2) 987 - 1000, April 1996.


Published: April 1996
First available in Project Euclid: 11 December 2002

zbMATH: 0862.60006
MathSciNet: MR1404540
Digital Object Identifier: 10.1214/aop/1039639374

Primary: 60B15
Secondary: 05A18 , 60J15

Keywords: enumeration , finite groups , Random walk , upper bound lemma

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 2 • April 1996
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