Limit theorems and absorption problems for one-dimensional correlated random walks

Limit theorems and absorption problems for quantum random walks in one dimension

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by 2 × 2 unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

Limit Theorems and Absorption Probrems for Quantum Random Walks in One Dimension

In this paper we review our recent results on limit theorems and absorption problems for the one-dimensional quantum random walk determined by 2× 2 unitary matrix.

Limit theorems for one and two-dimensional random walks in random scenery

Quenched Limit Theorems for Nearest Neighbour Random Walks in 1d Random Environment

It is well known that random walks in one dimensional random environment can exhibit subdiffusive behavior due to presence of traps. In this paper we show that the passage times of different traps are asymptotically independent exponential random variables with parameters forming, asymptotically, a Poisson process. This allows us to prove weak quenched limit theorems in the subdiffusive regime ...

A Local Limit Theorem for Random Walks in Balanced Environments

Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems — yielding a Gaussian density multiplied by a highly oscillatory modulating factor — for such models have been obtained. In the one-dimensional nearest-neighbor case with i.i.d. transition probabilities, local limits of uni...