The steps of a one-dimensional random walk are positive and occur randomly in time at a fixed mean rate. The sizes of the steps are independent and the size of each step has the same given probability ...

In a one-dimensional random walk, a “walker” is confined to a long, narrow path and moves forward or backward in steps according to the results of repeatedly tossing a coin. The walker takes a step in ...

For a one-dimensional simple random walk (St), for each time t we say a site x is a favorite site if it has the maximal local time. In this paper, we show that with probability 1 three favorite sites ...