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 constitute one of the cornerstone concepts in probability theory and statistical physics, representing a class of stochastic processes in which a moving entity takes successive steps in ...

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 ...

Let F(·) be a c.d.f. on [0,∞), f(s)=∑0 ∞ pjsj a p.g.f. with $p_{0}=0,\ 1 \alpha \equiv (\text{log}\ m)/(\text{log}\ \rho)$ there exists a unique solution H ...

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

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 ...

The nervous systems of foraging and predatory animals may prompt them to move along a special kind of random path called a Lévy walk to find food efficiently when no clues are available. It’s not ...