Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem
Abstract
For each β∈(0,+∞) there exists a canonical measure μβ on the ring Af of finite adeles. We show that the positive rationals act ergodically on (Af,μβ) for β∈(0,1], and then deduce from this the uniqueness of KMSβ-states for the Bost-Connes system.
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