When: Sunday, June 15,
10am
Where: Schreiber 309
Speaker: Matan Shalev,
Tel Aviv University
Title:
The Scaling Limit of Uniform Spanning Trees of Dense Graphs
In 1990, Aldous proved that the continuum random tree (CRT) is the scaling limit of the uniform spanning tree of the complete graph on n vertices. We consider uniform spanning trees on sequences of dense graphs converging to a graphon and show that, under appropriate rescaling, they also converge in distribution to Aldous' continuum random tree. Furthermore, we extract the precise scaling constant from the limiting graphon.
Based on joint works with Eleanor Archer and Asaf Nachmias.