We will show that the properly rescaled three-dimensional uniform spanning tree converges weakly with respect to a Gromov-Hausdorff-Prohorov-type topology in a space whose elements are measured, rooted real trees continuously embedded into Euclidean space. We will describe various properties of the intrinsic metrics, measures and embeddings of the limit in this space. This is based on a joint work with Omer Angel (UBC), David Croydon (Kyoto University) and Sarai Hernandez Torres (UBC).
Daisuke Shiraishi is a lecturer at Kyoto University, from which he received Ph.D. degree in Mathematics in 2012. His research interests focus on loop-erased random walk, uniform spanning tree and related topics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai