Please use this identifier to cite or link to this item:
http://arks.princeton.edu/ark:/88435/dsp01db78tg12p
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Sly, Allan | |
dc.contributor.author | Attwa, Yamaan | |
dc.date.accessioned | 2021-07-28T12:26:31Z | - |
dc.date.available | 2021-07-28T12:26:31Z | - |
dc.date.created | 2021-04-30 | |
dc.date.issued | 2021-07-28 | - |
dc.identifier.uri | http://arks.princeton.edu/ark:/88435/dsp01db78tg12p | - |
dc.description.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. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.title | Cutoff for random walk on k columns of hypercubes | |
dc.type | Princeton University Senior Theses | |
pu.date.classyear | 2021 | |
pu.department | Mathematics | |
pu.pdf.coverpage | SeniorThesisCoverPage | |
pu.contributor.authorid | 920191441 | |
pu.certificate | ||
pu.mudd.walkin | No | |
Appears in Collections: | Mathematics, 1934-2023 |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
ATTWA-YAMAAN-THESIS.pdf | 366.18 kB | Adobe PDF | Request a copy |
Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.