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math.DS2022
Nonamenable subforests of multi-ended quasi-pmp graphs
Ruiyuan Chen, Grigory Terlov, Anush Tserunyan
We prove the a.e. nonamenability of locally finite quasi-pmp Borel graphs whose every component admits at least three nonvanishing ends with respect to the underlying Radon--Nikody…
math.DS2022
A ratio ergodic theorem via tiling and uniformly syndetic markers
Benjamin D. Miller, Anush Tserunyan
We prove a purely Borel/measureless version of Dowker's ratio ergodic theorem, from which we derive a strengthening of Dowker's original theorem with a precise identification of th…