OxTalks will soon move to the new Halo platform and will become 'Oxford Events.' There will be a need for an OxTalks freeze. This was previously planned for Friday 14th November – a new date will be shared as soon as it is available (full details will be available on the Staff Gateway).
In the meantime, the OxTalks site will remain active and events will continue to be published.
If staff have any questions about the Oxford Events launch, please contact halo@digital.ox.ac.uk
Random planar maps have been studied from various aspects during the last 15 or 20 years, including various limiting distributions for several parameters of interest (such as the largest 2-connected component) and local Benjamini-Schramm limits as well as scaling limits. A pattern is a given planar map and we say that it appears in another map if it could be “cut out” just leaving a face. The simplest pattern is just a k-gon. It directly follows from the Benjamini-Schramm limit that the expected number of occurrences of a given pattern is asymptotically linear in the number of edges of the random map. However, it is a challenging problem to provide a more precise limit law. The purpose of this talk is to give a survey on the results and methods that have used so far in order to settle this question. It is conjectured that there is always a central limit theorem – and all results so far support this conjecture.