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
Consider a sequence of edge-weighted random graphs that converges in Benjamini-Schramm sense to a Unimodular Bienaymé Galton Watson tree with i.i.d weights on edges. If the weights are continuous, we prove that the joint distribution of the graphs and any maximum weight matching on the graphs also converges in Benjamini-Schramm sense to an identified joint distribution of the tree and a matching. The limiting joint distribution of the tree and the matching is characterised by the stationary measure of a message-passing algorithm. The proof is built upon Aldous’ original work on the random assignment problem.
We will also explore the case of maximal size maximum weight matchings as an extension and discuss a few open questions and conjectures.
This talk is based on a joint work with Nathanaël Enriquez, Laurent Ménard and Vianney Perchet.
