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) ...

We study the behavior of random walk in random environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ...

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 ...

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 ...

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 ...