6 papers
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…
Heavy repulsion of clusters in Bernoulli percolation
Sasha Bell, Tasmin Chu, Owen Rodgers +2
We study Bernoulli percolation on (non)unimodular quasi-transitive graphs and prove that, almost surely, for any two heavy clusters and , the set of vertices in wi…
Tree-like graphings, wallings, and median graphings of equivalence relations
Ruiyuan Chen, Antoine Poulin, Ran Tao +1
We prove several results showing that every locally finite Borel graph whose large-scale geometry is "tree-like" induces a treeable equivalence relation. In particular, our hypothe…