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 ...

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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 ...

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 ...