4 papers · 1 filter
The Radon--Nikodym topography of acyclic measured graphs
Anush Tserunyan, Robin Tucker-Drob
We study locally countable acyclic measure-class-preserving (mcp) Borel graphs by analyzing their "topography" -- the interaction between the geometry and the associated Radon--Nik…
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…
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…
A backward ergodic theorem along trees and its consequences for free group actions
Anush Tserunyan, Jenna Zomback
We prove a new pointwise ergodic theorem for probability-measure-preserving (pmp) actions of free groups, where the ergodic averages are taken over arbitrary finite subtrees of the…