48 citations · 169 across the 56 of their papers we have counts for
6 papers · 1 filter
Limits of subcritical random graphs and random graphs with excluded minors
Agelos Georgakopoulos, Stephan Wagner
We prove local convergence results for the uniformly random, labelled or unlabelled, graphs from subcritical families. As an example special case, we prove Benjamini-Schramm conver…
Hyperbolicity vs. Amenability for planar graphs
Bruno Federici, Agelos Georgakopoulos
The aim of this paper is to clarify the relationship between Gromov-hyperbolicity and amenability for planar maps.
The planar Cayley graphs are effectively enumerable I: consistently planar graphs
Agelos Georgakopoulos, Matthias Hamann
We obtain an effective enumeration of the family of finitely generated groups admitting a faithful, properly discontinuous action on some 2-manifold contained in the sphere. This i…
Group-Walk Random Graphs
Agelos Georgakopoulos
We introduce a construction that gives rise to a variety of "geometric" finite random graphs, and describe connections to the Poisson boundary, Naim's kernel, and Sznitman's random…
On covers of graphs by Cayley graphs
Agelos Georgakopoulos
We prove that every vertex transitive, planar, 1-ended, graph covers every graph whose balls of radius r are isomorphic to the ball of radius r in G for a sufficiently large r. We…
Every planar graph with the Liouville property is amenable
Johannes Carmesin, Agelos Georgakopoulos
We introduce a strengthening of the notion of transience for planar maps in order to relax the standard condition of bounded degree appearing in various results, in particular, the…