5 papers
A study of 2-ended graphs via harmonic functions
Agelos Georgakopoulos, Alex Wendland
We prove that every recurrent graph quasi-isometric to admits an essentially unique Lipschitz harmonic function . If is vertex-transitive, then the action o…
Presentations for Vertex Transitive Graphs
Agelos Georgakopoulos, Matthias Hamann, Alex Wendland
We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion o…
From the Bernoulli Factory to a Dice Enterprise via Perfect Sampling of Markov Chains
Giulio Morina, Krzysztof Latuszynski, Piotr Nayar +1
Given a -coin that lands heads with unknown probability , we wish to produce an -coin for a given function . This problem is commonly known…
2-Groups, 2-Characters, and Burnside Rings
Dmitriy Rumynin, Alex Wendland
We study 2-representations, i.e., actions of 2-groups on 2-vector spaces. Our main focus is character theory for 2-representations. To this end we employ the technique of extended…
Colouring of plane graphs with unique maximal colours on faces
Alex Wendland
The Four Colour Theorem asserts that the vertices of every plane graph can be properly coloured with four colors. Fabrici and Göring conjectured the following stronger statement to…