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math.DS2025
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…
math.PR2025
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…