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math.PR2023
The critical percolation probability is local
Philip Easo, Tom Hutchcroft
We prove Schramm's locality conjecture for Bernoulli bond percolation on transitive graphs: If is a sequence of infinite vertex-transitive graphs converging local…
math.GR2023
Uniform finite presentation for groups of polynomial growth
Philip Easo, Tom Hutchcroft
We prove a quantitative refinement of the statement that groups of polynomial growth are finitely presented. Let be a group with finite generating set and let $\operatornam…
math.PR2023
Double-exponential susceptibility growth in Dyson's hierarchical model with interaction
Philip Easo, Tom Hutchcroft, Jana Kurrek
We study long-range percolation on the -dimensional hierarchical lattice, in which each possible edge is included independently at random with inclusion probability $1…