17 citations · 61 across the 21 of their papers we have counts for
26 papers
The Almost Finite--Purely Infinite Dichotomy for Minimal Amenable Ample Groupoids
Gábor Elek, Ádám Timár
We answer, in the principal setting, a question of Matui on the almost finite--purely infinite dichotomy for minimal amenable ample groupoids. We prove that a second-countable Haus…
Finitely dependent random colorings of bounded degree graphs
Ádám Timár
We prove that every (possibly infinite) graph of degree at most has a 4-dependent random proper -coloring, and one can construct it as a finitary factor of iid. F…
Strong almost finiteness
Gábor Elek, Ádám Timár
A countable, bounded degree graph is almost finite if it has a tiling with isomorphic copies of finitely many Følner sets, and we call it strongly almost finite, if the tiling can…
Factor of iid's through stochastic domination
Ádám Timár
We develop a method to prove that certain percolation processes on amenable random rooted graphs are factors of iid (fiid), given that the process is a monotone limit of random fin…
A factor matching of optimal tail between Poisson processes
Adam Timar
Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension at least 3. We construct a perfect matching between the two point sets th…
Invariant embeddings of unimodular random planar graphs
Itai Benjamini, Adam Timar
Consider an ergodic unimodular random one-ended planar graph $\G$ of finite expected degree. We prove that it has an isometry-invariant locally finite embedding in the Euclidean pl…