Mathematical analysis reveals the free critical exponent in localized Bost-Connes systems, indicating how phase transitions persist under free independence.
The free-probabilistic variant of the localized Bost-Connes construction is built, replacing the tensor independence of the prime coordinates by free independence. The free critical exponent is identified and compared with the classical one, and the extent to which the phase-transition picture of the foundational paper survives free independence is determined.
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Ruqing Chen (2026) studied this question.
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