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

Evita Nestoridi

doi:10.1016/j.jalgebra.2018.10.037

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

Evita Nestoridi

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English (US)
Pages (from-to)	97-113
Number of pages	17
Journal	Journal of Algebra
Volume	521
DOIs	https://doi.org/10.1016/j.jalgebra.2018.10.037
State	Published - 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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10.1016/j.jalgebra.2018.10.037

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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.",

keywords = "Comparison theory, Mixing time, Random walks on groups, Super-character theory, Super-classes, Upper triangular matrices",

author = "Evita Nestoridi",

note = "Funding Information: This paper is adapted from my PhD thesis, for the completion of which I was supported by Stanford University . Publisher Copyright: {\textcopyright} 2018",

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AB - 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.

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KW - Random walks on groups

KW - Super-character theory

KW - Super-classes

KW - Upper triangular matrices

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ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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