Title, abstract and the zoom link are below the signature and can be found on the website https://www.owprobability.org/one-world-probability-seminar.

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The GHP scaling limit of uniform spanning trees in high dimensions.

Eleanor Archer (Dauphine-PSL Paris)

A spanning tree of a finite connected graph G is a connected subgraph of G that contains every vertex and no cycles. A well-known result of Aldous states that the scaling limit of the uniform spanning tree (UST) of the complete graph is the Brownian continuum random tree. We will discuss a recent result that shows that this is a universal phenomenon, in that the GHP scaling limit of the UST of any appropriate sequence of high dimensional graphs is the CRT. In particular, this holds for the torus in dimensions five and higher.

Based on joint work with Asaf Nachmias and Matan Shalev.

Scaling limit of the Aldous-Broder chain on regular graphs: the transient regime.

Anita Winter (Duisburg-Essen University)

A spanning tree of a finite connected graph G is a connected subgraph of G that contains every vertex and no cycles. A well-known way to generate a uniform spanning tree (UST) is the Aldous-Broder algorithm. This is a stochastic process with values in rooted trees that is driven by a random walk on G and converges as time goes to infinity towards the Brownian Continuum Tree (CRT). On the complete graph it is known that this process has a GH-scaling limit which is referred to as Root Growth with Regrafting dynamics (RGRG). We will show that this is again a universal phenomenon, i.e., it holds for the Alous-Broder chain on any appropriate sequence of regular graphs in the transient regime. In particular, this holds for the torus in dimensions five and higher.

This is joint work with Osvaldo Angtuncio Hernandez and Gabriel Berzunza Ojeda.