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dc.contributor.advisorSly, Allan
dc.contributor.authorAttwa, Yamaan
dc.description.abstractWe 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.titleCutoff for random walk on k columns of hypercubes
dc.typePrinceton University Senior Theses
Appears in Collections:Mathematics, 1934-2021

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