Multicoloured Random Graphs: Constructions and Symmetry
arXiv:1406.7870
Abstract
This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the emphasis is on understanding those groups that are supported by these graphs together with links with other structures such as lattices, topologies and filters, rings and algebras, metric spaces, sets and models, Moufang loops and monoids. The large amount of background material included serves as an introduction to the theories that are used to produce the new results. The large number of references should help in making this a resource for anyone interested in beginning research in this or allied fields.
Index added in v2. This is the first of 3 documents; the other 2 will appear in physics
References in corpus (11)
- Statistical mechanics of complex networks
- Graph limits and exchangeable random graphs
- A General Formalism for Inhomogeneous Random Graphs
- (Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks
- Sylow's theorem for Moufang loops
- Closed subgroups of the infinite symmetric group
- The Profile of relations
- Hopf Algebras of Graphs
- Automorphism groups of saturated structures; a review
- Random graph gauge theories as toy models for non-perturbative string theories
- Universal and ultrahomogeneous Polish metric structures