Random walks in noninteger dimension

@article{Bender1994RandomWI,
  title={Random walks in noninteger dimension},
  author={C. Bender and S. Boettcher and L. Mead},
  journal={Journal of Mathematical Physics},
  year={1994},
  volume={35},
  pages={368-388}
}
  • C. Bender, S. Boettcher, L. Mead
  • Published 1994
  • Mathematics, Physics
  • Journal of Mathematical Physics
  • One can define a random walk on a hypercubic lattice in a space of integer dimension D. For such a process formulas can be derived that express the probability of certain events, such as the chance of returning to the origin after a given number of time steps. These formulas are physically meaningful for integer values of D. However, these formulas are unacceptable as probabilities when continued to noninteger D because they give values that can be greater than 1 or less than 0. In this paper a… CONTINUE READING

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