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 ...

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) ...

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 ...