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) ...

Quantum walks sound abstract, but they sit at the center of a very concrete race: who will harness quantum mechanics to solve ...

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 ...