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 ...

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 ...

Random walks in random environments constitute a pivotal area of research at the interface of probability theory, statistical physics and mathematical modelling. This field investigates stochastic ...

Juggling competing demands in a network of feverishly calculating computers drawing on the same memory resources is like trying to avert collisions among blindfolded, randomly zigzagging ice skaters.

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 ...

That was the “classical” random walk - which just means when we described it, we did not have to use any quantum mechanics. To describe a “quantum” random walk, we replace our coin with a quantum coin ...