Measured expanders

Li K, Spakula J, Zhang J (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Journal of Topology and Analysis World Scientific Publishing Co. Pte Ltd

DOI: 10.1142/S1793525322500078

Abstract

By measured graphs, we mean graphs endowed with a measure on the set of vertices. In this context, we explore the relations between the appropriate Cheeger constant and Poincare inequalities. We prove that the so-called Cheeger inequality holds in two cases: when the measure comes from a random walk, or when the measure has a bounded measure ratio. Moreover, we also prove that our measured (asymptotic) expanders are generalised expanders introduced by Tessera. Finally, we present some examples to demonstrate relations and differences between classical expander graphs and the measured ones. This paper is motivated primarily by our previous work on the rigidity problem for Roe algebras.

Authors with CRIS profile

Kang Li Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

Fudan University / 复旦大学 CN China (CN) University of Southampton GB United Kingdom (GB)

How to cite

APA:

Li, K., Spakula, J., & Zhang, J. (2022). Measured expanders. Journal of Topology and Analysis. https://dx.doi.org/10.1142/S1793525322500078

MLA:

Li, Kang, Jan Spakula, and Jiawen Zhang. "Measured expanders." Journal of Topology and Analysis (2022).

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