### Abstract

We consider the problem of derandomizing random walks in the Euclidean space ℝ^{k}. We show that for k = 2, and in some cases in higher dimensions, such walks can be simulated in Logspace using only poly-logarithmically many truly random bits. As a corollary, we show that the Dirichlet Problem can be deterministically simulated in space O(log n √log log n), where 1/n is the desired precision of the simulation.

Original language | English (US) |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization |

Subtitle of host publication | Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings |

Publisher | Springer Verlag |

Pages | 353-365 |

Number of pages | 13 |

ISBN (Print) | 9783540742074 |

DOIs | |

State | Published - 2007 |

Externally published | Yes |

Event | 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 - Princeton, NJ, United States Duration: Aug 20 2007 → Aug 22 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4627 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 |
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Country | United States |

City | Princeton, NJ |

Period | 8/20/07 → 8/22/07 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Binder, I., & Braverman, M. (2007). Derandomization of euclidean random walks. In

*Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings*(pp. 353-365). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-74208-1_26