Measured expanders

Li K, Spakula J, Zhang J (2022)

Publication Type: Journal article

Publication year: 2022


DOI: 10.1142/S1793525322500078


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.

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Li, K., Spakula, J., & Zhang, J. (2022). Measured expanders. Journal of Topology and Analysis.


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

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