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) ...

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 ...

The last time I looked at random walks, I used them to calculate the value of Pi for Pi Day. But what is a random walk, really? A mathematician will tell you that it's a stochastic process—a path ...

The random walk theorem, first presented by French mathematician Louis Bachelier in 1900 and then expanded upon by economist Burton Malkiel in his 1973 book A Random Walk Down Wall Street, asserts ...

Albert Phung has 7+ years of experience as a process improvement consultant for several businesses; currently with Alberta Health Services. Suzanne is a content marketer, writer, and fact-checker. She ...