Weak limits for quantum random walks.

@article{Grimmett2004WeakLF,
  title={Weak limits for quantum random walks.},
  author={Geoffrey R. Grimmett and Svante Janson and Petra F. Scudo},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2004},
  volume={69 2 Pt 2},
  pages={
          026119
        }
}
  • G. Grimmett, S. Janson, P. Scudo
  • Published 2004
  • Mathematics, Medicine, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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--> infinity 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. 
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