Let {Xk: k ≥ 1} be a sequence of independent, identically distributed random variables with $EX_{1} = \mu < 0$. Form the random walk {Sn : n ≥ 0} by setting S0 ...

In the classical simple random walk the steps are independent, that is, the walker has no memory. In contrast, in the elephant random walk, which was introduced by Schütz and Trimper [19] in 2004, the ...

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 ...

Research of the probability and statistics group includes particle systems, theoretical statistics, non-conventional random walks, random matrix theory, and random polynomials. Research interests also ...

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 ...