17 citations · 61 across the 21 of their papers we have counts for
18 papers · 1 filter
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…
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…
Unimodular random one-ended planar graphs are sofic
Adam Timar
We prove that if a unimodular random graph is almost surely planar and has finite expected degree, then it has a combinatorial embedding into the plane which is also unimodular. Th…
One-ended spanning trees in amenable unimodular graphs
Adam Timar
We prove that every amenable one-ended Cayley graph has an invariant spanning tree of one end. More generally, for any 1-ended amenable unimodular random graph we construct a facto…