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 ...

Interest rates are inherently difficult to predict, and the simple random walk benchmark has proven hard to beat. But macroeconomics can help, because the long-run trend in interest rates is driven by ...

An interesting paper making the point that you can too forecast foreign exchange rates. Not, of course, at the hour to hour level where people speculate at leverage of 500:1, but over longer time ...

The pharmaceutical research that makes the news tends to focus on single "blockbuster" drugs. Some of the most effective therapies, in contrast, are combinations of drugs. These combinations can often ...