A super-class walk on upper-triangular matrices

A Super-class Walk on Upper-triangular Matrices

Let G be the group of n×n upper-triangular matrices with elements in a finite field and ones on the diagonal. This paper applies the character theory of Andre, Carter and Yan to analyze a natural random walk based on adding or subtracting a random row from the row above.

A SUPER - CLASS WALK ON UPPER - TRIANGULAR MATRICESEry

Random walk on upper triangular matrices mixes rapidly

We present an upper bound O(n2) for the mixing time of a simple random walk on upper triangular matrices. We show that this bound is sharp up to a constant, and find tight bounds on the eigenvalue gap. We conclude by applying our results to indicate that the asymmetric exclusion process on a circle indeed mixes more rapidly than the corresponding symmetric process.

Multiplicative Functional on Upper Triangular Fuzzy Matrices

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal element...

Two Random Walks on Upper Triangular Matrices

We study two random walks on a group of upper triangular matrices. In each case, we give upper bound on the mixing time by using a stopping time technique.