A Super-class Walk on Upper-triangular Matrices

A SUPER - CLASS WALK ON UPPER - TRIANGULAR MATRICESEry

Mixing of the Upper Triangular Matrix Walk

We study a natural random walk over the upper triangular matrices, with entries in the field Z2, generated by steps which add row i + 1 to row i. We show that the mixing time of the lazy random walk is O(n) which is optimal up to constants. Our proof makes key use of the linear structure of the group and extends to walks on the upper triangular matrices over the fields Zq for q prime.

On the fine spectrum of generalized upper triangular double-band matrices $Delta^{uv}$ over the sequence spaces $c_o$ and $c$

The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular double-band matrices uv over the sequence spaces c0 and c. These results are more general than the spectrum of upper triangular double-band matrices of Karakaya and Altun[V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics...

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.

Random Walk on Uppertriangular Matrices Mixes

We present an upper bound O(n 2) 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 nd 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.