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`http://arks.princeton.edu/ark:/88435/dsp01db78tg12p`

Title: | Cutoff for random walk on k columns of hypercubes |

Authors: | Attwa, Yamaan |

Advisors: | Sly, Allan |

Department: | Mathematics |

Certificate Program: | |

Class Year: | 2021 |

Abstract: | We consider the random walk on a $n \times k$ matrix over $\mathbf{F}_2$ which moves by picking an ordered pair $(i, j)$ of distinct $i,j \in [n]$ and updating row $j$ by adding row $i$ mod(2). The state space of the random walk is the set of $n \times k$ matrices with linearly independent columns. We attempt to show that the hamming weight of this random walk exhibits a total-variation cutoff (in n) at $\frac{3}{2} n \log n$ with a window of size $n$. We conclude this work with a possible approach to generalize the same cutoff to the original random walk. This paper is meant as a generalization of a result of Ben-Hamou and Peres. Their paper correspond to the one column case, which is the originless $n$-dimensional hypercube. The aforementioned paper will be reviewed in this work, as some results, including the main one, will be used here. |

URI: | http://arks.princeton.edu/ark:/88435/dsp01db78tg12p |

Type of Material: | Princeton University Senior Theses |

Language: | en |

Appears in Collections: | Mathematics, 1934-2021 |

Files in This Item:

File | Description | Size | Format | |
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ATTWA-YAMAAN-THESIS.pdf | 366.18 kB | Adobe PDF | Request a copy |

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