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 ...

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 ...

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 ...

Computer scientists have only begun to realize the potential of quantum computing and algorithms, where computers use quantum principles to store data in qubits. One thing that could help in the ...

University of Chicago mathematician Gregory Lawler has been awarded the prestigious Wolf Prize for pioneering research that helped expand the field of probability into new disciplines. Awarded by the ...