Weak limits for quantum random walks
Grimmett, Geoffrey ; Janson, Svante ; Scudo, Petra
arXiv, 0309135 / Harvested from arXiv
Text on arXiv
We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With $X_n$ denoting position at time $n$, we show that $X_n/n$ converges weakly as $n \to \infty$ to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain preceding derivations valid in one dimension that make use of combinatorial and path integral methods.
Publié le : 2003-09-18
Classification:  Quantum Physics,  Mathematical Physics,  Mathematics - Probability 
@article{0309135,
     author = {Grimmett, Geoffrey and Janson, Svante and Scudo, Petra},
     title = {Weak limits for quantum random walks},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0309135}
}

Grimmett, Geoffrey; Janson, Svante; Scudo, Petra. Weak limits for quantum random walks. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0309135/