We study limit laws for simple random walks on supercritical long-range percolation clusters on ℤ d , d ≥ 1. For the long range percolation model, the probability that two vertices x, y are connected ...

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 ...

Theory that stock price changes from day to day are accidental or haphazard; changes are independent of each other and have the same probability distribution. For a simple random walk, the best ...