### Abstract

We analyse Jim Propp's P-machine, a simple deterministic process that simulates a random walk on ℤ ^{d} to within a constant. The proof of the error bound relies on several estimates in the theory of simple random walks and some careful summing. We mention three intriguing conjectures concerning sign-changes and unimodality of functions in the linear span of {p(.,x): x ∈ ℤ ^{d}}where p(n, x) is the probability that a walk beginning from the origin arrives at x at time n.

Original language | English (US) |
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Pages (from-to) | 815-822 |

Number of pages | 8 |

Journal | Combinatorics Probability and Computing |

Volume | 15 |

Issue number | 6 |

DOIs | |

State | Published - Nov 1 2006 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

Cooper, J. N., & Spencer, J. (2006). Simulating a random walk with constant error.

*Combinatorics Probability and Computing*,*15*(6), 815-822. https://doi.org/10.1017/S0963548306007565