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 ...

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 ...

In this paper, we introduce a new simple but powerful general technique for the study of edge- and vertex-reinforced processes with super-linear reinforcement, based on the use of order statistics for ...

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 ...

For a random walk with drift, the best forecast of tomorrow's price is today's price plus a drift term. One could think of the drift as measuring a trend in the price (perhaps reflecting long-term ...

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 ...