### 抜粋

Motivated by a derandomization of Markov chain Monte Carlo (MCMC), this paper investigates deterministic random walks, which is a deterministic process analogous to a random walk. While there are some progress on the analysis of the vertex-wise discrepancy (i.e., L_{∞} discrepancy), little is known about the total variation discrepancy (i.e., Li discrepancy), which plays a significant role in the analysis of an FPRAS based on MCMC. This paper investigates upper bounds of the L_{1} discrepancy between the expected number of tokens in a Markov chain and the number of tokens in its corresponding deterministic random walk. First, we give a simple but nontrivial upper bound O(mt∗) of the L_{1} discrepancy for any ergodic Markov chains, where m is the number of edges of the transition diagram and t∗ is the mixing time of the Markov chain. Then, we give a better upper bound O(m√t∗ log t∗) for non-oblivious deterministic random walks, if the corresponding Markov chain is ergodic and lazy. We also present some lower bounds.

元の言語 | 英語 |
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ホスト出版物のタイトル | 13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016 |

編集者 | James Allen Fill, Mark Daniel Ward |

出版者 | Society for Industrial and Applied Mathematics Publications |

ページ | 138-148 |

ページ数 | 11 |

ISBN（電子版） | 9781510819696 |

DOI | |

出版物ステータス | 出版済み - 2016 |

イベント | 13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016 - Arlington, 米国 継続期間: 1 11 2016 → … |

### 出版物シリーズ

名前 | 13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016 |
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### その他

その他 | 13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016 |
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国 | 米国 |

市 | Arlington |

期間 | 1/11/16 → … |

### All Science Journal Classification (ASJC) codes

- Applied Mathematics
- Materials Chemistry
- Discrete Mathematics and Combinatorics

## フィンガープリント Total variation discrepancy of deterministic random walks for ergodic Markov chains' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016*(pp. 138-148). (13th Workshop on Analytic Algorithmics and Combinatorics 2016, ANALCO 2016). Society for Industrial and Applied Mathematics Publications. https://doi.org/10.1137/1.9781611974324.13