The classical Baum-Connes assembly map is quantitatively an isomorphism for lacunary hyperbolic groups containing large-girth graph sequences in their Cayley graphs.
Examples of random groups
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Controlled Analytic Properties and the Quantitative Baum-Connes Conjecture
The classical Baum-Connes assembly map is quantitatively an isomorphism for lacunary hyperbolic groups containing large-girth graph sequences in their Cayley graphs.