A Non-Symmetric Kesten Criterion and Ratio Limit Theorem for Random Walks on Amenable Groups

Dougall, Rhiannon; Sharp, Richard

Abstract

We consider random walks on countable groups. A celebrated result of Kesten says that the spectral radius of a symmetric walk (whose support generates the group as a semigroup) is equal to one if and only if the group is amenable. We give an analogue of this result for walks that are not symmetric. We also conclude a ratio limit theorem for amenable groups.

Citation

Dougall, R., & Sharp, R. (2024). A Non-Symmetric Kesten Criterion and Ratio Limit Theorem for Random Walks on Amenable Groups. International Mathematics Research Notices, 2024(7), 6209-6223. https://doi.org/10.1093/imrn/rnae014

• Journal Article Type: Article
• Acceptance Date: Jan 17, 2024
• Online Publication Date: Feb 12, 2024
• Publication Date: Apr 8, 2024
• Deposit Date: Apr 8, 2024
• Publicly Available Date: Apr 8, 2024
• Journal: International Mathematics Research Notices
• Print ISSN: 1073-7928
• Electronic ISSN: 1687-0247
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 2024
• Issue: 7
• Pages: 6209-6223
• DOI: https://doi.org/10.1093/imrn/rnae014
• Keywords: General Mathematics
• Public URL: https://durham-repository.worktribe.com/output/2379874