In the plane, we define a fractal known as the Vicsek snowflake in terms of a family of affine contractions in 2. We show that the Vicsek snowflake is a nested fractal in the sense of Lindstrøm (1990). We define random walks on the Vicsek snowflake and explicitly find an invariant probability...

Consider the class of discrete time, general state space Markov chains which satisfy a "uniform ergodicity under sampling" condition. There are many ways to quantify the notion of "mixing time", i.e., time to approach stationarity from a worst initial state. We prove results asserting...

Recent works by Newell [13] and Coffman. [2] have studied a queuing or storage model which is most easily visualized as the process of parkins cars in a parking lot where customers park as close as they can to some fixed point. This paper describes several space-time processes which arise as...