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.

Continuous-time mixes represent a relatively new field in anonymity services. Their simplicity and probabilistic approach suggest promising results. In this paper their two most recent representatives, the SG Mix and the PROB Channel will be analysed. The aim of this paper is twofold: first it will be shown via analytical means that considering a locally back-tracing observer and the source-hid...