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 prove that, under the assumption of quasi-transitivity, if a branching random walk on ℤd survives locally (at arbitrarily large times there are individuals alive at the origin), then ...

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.

Sample space, Field and Probability Measure. Axiomatic definition of Probability. Bayes' theorem. Repeated trials. Continuous and discrete random variables and their probability distribution and ...

Physicists in Austria have demonstrated a “quantum walk” in detail for the first time, using trapped ions. Such experiments could allow us to better understand the transition between the quantum and ...