Related papers: Correction: Limit theorems for coupled continuous …
The continuous time random walks (CTRWs) are typically defned in the way that their trajectories are discontinuous step fuctions. This may be a unwellcome feature from the point of view of application of theese processes to model certain…
Correction to Annals of Probability 28 (2000) 277--302 [doi:10.1214/aop/1019160120].
There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between…
This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].
We study the disordered quantum walk in one dimension, and obtain the weak limit theorem.
The Annals of Applied Probability (2002) 12 1114-1137
We derive the continuous-time limit of discrete quantum walks with topological phases. We show the existence of a continuous-time limit that preserves their topological phases. We consider both simple-step and split-step walks, and derive…
We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random walk are integer-valued, centered, with a third moment equal to…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
We extend the construction given by [Chisaki et.al, arXiv:1009.1306v1] from lines to planes, and obtain the associated limit theorems for quantum walks on such a graph.
This note contains old instead of new results about random walks on groups, which may serve as a small supplement to the author's monograph ``Random Walks on Infinite Graphs and Groups'' (Cambridge Univ. Press 2000/2009). First, we exhibit…
We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…
Functional limit theorem for continuous-time random walks (CTRW) are found in general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional…
The method of the quantum probability theory only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. In the present…
We consider a symmetric random walk on the $\nu$-dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central limit theorem for this process. A short-range correction…
Correction to Annals of Probability 29 (2001) 1612--1624 [doi:10.1214/aop/1015345764].
We consider random walks perturbed at zero which behave like (possibly different) random walks with i.i.d. increments on each half lines and restarts at $0$ whenever they cross that point. We show that the perturbed random walk, after being…
We correct the proofs of the main theorems in our paper "Limit theorems for Betti numbers of random simplicial complexes".
We investigate random walks on the general linear group constrained within a specific domain, with a focus on their asymptotic behavior. In a previous work [38], we constructed the associated harmonic measure, a key element in formulating…
A quantum central limit theorem for a continuous-time quantum walk on a homogeneous tree is derived from quantum probability theory. As a consequence, a new type of limit theorems for another continuous-time walk introduced by the walk is…