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Consider the random walk on the $n \times n$ upper triangular matrices with ones on the diagonal and elements over $\mathbb{F}_p$ where we pick a row at random and either… Click to show full abstract
Consider the random walk on the $n \times n$ upper triangular matrices with ones on the diagonal and elements over $\mathbb{F}_p$ where we pick a row at random and either add it or subtract it from the row directly above it. The main result of this paper is to prove that the dependency of the mixing time on $p$ is $p^2$. This is proven by combining super-character theory and comparison theory arguments.
Keywords:
random walk;
triangular matrices;
character theory;
upper triangular;
super character;
theory comparison
Journal Title: Journal of Algebra
Year Published: 2019
Link to full text (if available)
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Journal Title: Journal of Algebra
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!