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 ...

Random walks constitute a fundamental model in probability theory, widely employed to elucidate diffusion processes and random fluctuations in disordered systems. The Gaussian free field (GFF) ...

Why is it that when you walk randomly, the more you walk, the farther you get from your starting point? The Quanta Newsletter ...

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 ...