### 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) |
---|---|

Pages (from-to) | 815-822 |

Number of pages | 8 |

Journal | Combinatorics Probability and Computing |

Volume | 15 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2006 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Statistics and Probability

### Cite this

*Combinatorics Probability and Computing*,

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

**Simulating a random walk with constant error.** / Cooper, Joshua N.; Spencer, Joel.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 15, no. 6, pp. 815-822. https://doi.org/10.1017/S0963548306007565

}

TY - JOUR

T1 - Simulating a random walk with constant error

AU - Cooper, Joshua N.

AU - Spencer, Joel

PY - 2006/11

Y1 - 2006/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33750363378&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750363378&partnerID=8YFLogxK

U2 - 10.1017/S0963548306007565

DO - 10.1017/S0963548306007565

M3 - Article

VL - 15

SP - 815

EP - 822

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 6

ER -