Sofic entropy and amenable groups
β Scribed by BOWEN, LEWIS
- Book ID
- 115313351
- Publisher
- Cambridge University Press
- Year
- 2011
- Tongue
- English
- Weight
- 695 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0143-3857
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## Abstract We prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V. Mathai, T. Schick, and S. Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we define integer operators and prove a quantiza
We prove that an ergodic free action of a countable discrete amenable group with completely positive entropy has a countable Lebesgue spectrum. Our approach is based on the Rudolph-Weiss result on the equality of conditional entropies for actions of countable amenable groups with the same orbits. Re