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math.PR2019★ 4 cited
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…
math.PR2019
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…