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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Quantum walks explained, and why they could change everything
Quantum walks sound abstract, but they sit at the center of a very concrete race: who will harness quantum mechanics to solve problems that overwhelm today’s most powerful supercomputers. Instead of ...
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 ...
Why is it that when you walk randomly, the more you walk, the farther you get from your starting point? The Quanta Newsletter ...
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