We consider a random walker on a d-regular graph. Starting from a fixed vertex, the first step is a unit step in any one of the d directions, with common probability 1/d for each one. At any later ...

In this paper we provide further results on the general d-dimensional correlated random walk. In particular, we prove that the n-step characteristic function of any correlated random walk satisfies a ...

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 ...

Mathematics professor Gregory Lawler was named a co-winner of the $100,000 Wolf Prize. The award recognizes Lawler’s research in probability theory involving random walks and Brownian motion, which ...

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.

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 ...