Quantum walks, the quantum analogue of classical random walks, have emerged as a pivotal framework in the study of quantum dynamics and information processing. These systems exploit inherently quantum ...

Consider the number of steps needed by algorithms to locate the minimum of functions defined on the d-cube, where the functions are known to have no local minima except the global minimum. Regard this ...

Random walks constitute one of the cornerstone concepts in probability theory and statistical physics, representing a class of stochastic processes in which a moving entity takes successive steps in ...

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk ...