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 foundational concept in probability theory, describing the seemingly erratic movement of particles or agents as they traverse a space in a series of stochastic steps. In many ...

Quantum walks are changing the way scientists think about computation. They use the strange and powerful rules of quantum physics—such as superposition, interference, and entanglement—to solve ...

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 ...

Why is it that when you walk randomly, the more you walk, the farther you get from your starting point? The Quanta Newsletter ...

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 ...