The random walk on upper triangular matrices over \(\mathbb{Z} / m\mathbb{Z}\)

DOI10.1007/s00440-023-01228-2zbMath1530.60043arXiv2012.08731OpenAlexW3110683778MaRDI QIDQ6070361

Evita Nestoridi, Allan Sly

Publication date: 20 November 2023

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.08731

zbMATH Keywords

Markov chainsrandom walksupper triangular matricesmixing times

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Sums of independent random variables; random walks (60G50) Discrete-time Markov processes on general state spaces (60J05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Continuous-time Markov processes on discrete state spaces (60J27)

Cites Work

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• An exercise(?) in Fourier analysis on the Heisenberg group
• Cutoff for the East process
• Translated Poisson approximation using exchangeable pair couplings
• Basic characters of the unitriangular group (for arbitrary primes)
• Random walk on unipotent matrix groups
• Upper triangular matrix walk: Cutoff for finitely many columns