The random walk on upper triangular matrices over Z/ mZ

Evita Nestoridi; Allan Sly

doi:10.1007/s00440-023-01228-2

The random walk on upper triangular matrices over Z/ mZ

Evita Nestoridi, Allan Sly

Mathematics

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

Abstract

We study a natural random walk on the n× n uni-upper triangular matrices, with entries in Z/ mZ , generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this random walk is O(m²nlog n+ n²m^o⁽¹⁾) . This answers a question of Stong and of Arias-Castro, Diaconis, and Stanley.

Original language	English (US)
Pages (from-to)	571-601
Number of pages	31
Journal	Probability Theory and Related Fields
Volume	187
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-023-01228-2
State	Published - Dec 2023

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Markov chains
Mixing times
Upper triangular matrices

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10.1007/s00440-023-01228-2

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AB - We study a natural random walk on the n× n uni-upper triangular matrices, with entries in Z/ mZ , generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this random walk is O(m2nlog n+ n2mo(1)) . This answers a question of Stong and of Arias-Castro, Diaconis, and Stanley.

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The random walk on upper triangular matrices over Z/ mZ

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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