46 citations · 164 across the 25 of their papers we have counts for
5 papers · 1 filter
Qualitative graph limit theory. Cantor Dynamical Systems and Constant-Time Distributed Algorithms
Gábor Elek
The goal of the paper is to lay the foundation for the qualitative analogue of the classical, quantitative sparse graph limit theory. In the first part of the paper we introduce th…
Free minimal actions of countable groups with invariant probability measures
Gábor Elek
We prove that for any countable group G there exists a free minimal continuous action of G on the Cantor set admitting an invariant Borel probability measure.
On universal continuous actions on the Cantor set
Gábor Elek
Using the notion of proper Cantor colorings we prove the following theorem. For any countably infinite group , there exists a free continuous action on…
Amenable purely infinite actions on the non-compact Cantor set
Gabor Elek
We prove that any countable non-amenable group G admits a free minimal amenable purely infinite action on the non-compact Cantor set. This answers a question of Kellerhals, Monod a…
Cantor combinatorics and almost finiteness
Gabor Elek
In this survey we give a concise introduction to a continuous version of Borel combinatorics. Our approach will have a certain algorithm-theoretic nature and we will give special e…