IJPAM: Volume 54, No. 2 (2009)

EXTENSION OF A RANDOM WALK ON
FINITE ABELIAN GROUPS

Joseph McCollum
Department of Quantitative Business Analysis
Siena College
515, Loudon Road, Loudonville, NY 12211, USA
e-mail: [email protected]


Abstract.In the survey articles written by M. Hildebrand and L. Saloff-Coste, there is a good overview of some known results in the theory of random walks on finite groups. One result of interest focuses on an Abelian group $G$ with $n$ elements such that $n=n_1 \cdots n_t$ where $n_1 \ge \cdots \ge n_t$ are prime numbers. Plus, $t \le L$ for some value $L$ not depending on $n$, and $n_1 \le An_t$ for some value $A$ not depending on $n$. It was shown by C. Dou that a $k$ element set chosen uniformly from all subsets of $G$ will create a random walk that will converge to the uniform distribution. This paper will extend this result to a larger class of groups by changing the restrictions.

Received: June 3, 2009

AMS Subject Classification: 60G50

Key Words and Phrases: random walk, Abelian groups

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 2