Super-character theory and comparison arguments for a random walk on the upper triangular matrices

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Abstract

Consider the random walk on the n×n upper triangular matrices with ones on the diagonal and elements over Fp 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 p2. This is proven by combining super-character theory and comparison theory arguments.

Original languageEnglish (US)
Pages (from-to)97-113
Number of pages17
JournalJournal of Algebra
Volume521
DOIs
StatePublished - Mar 1 2019

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Comparison theory
  • Mixing time
  • Random walks on groups
  • Super-character theory
  • Super-classes
  • Upper triangular matrices

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