Abstract
The relationship between index theory and random walks on fusion algebras is discussed. Popa's notion of amenability is reformulated as a property of fusion algebras, and several equivalent conditions of amenability are obtained. A ratio limit theorem is proved as a characterization of amenability. A number of conditions, all equivalent to Popa's notion of strong amenability in the case of subfactors, of a pair of a fusion algebra and a probability measure are proposed, and their relationship is studied from the viewpoint of random walks and entropic densities. Fusion algebra homomorphisms and free products of fusion algebras are also discussed.
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