The uniform spanning forests (USFs) of infinite an infinite graph G are defined as infinite volume limits of uniform spanning trees on finite subgraphs of G. In this talk, I will describe how we use a new way of sampling the USF using the random interlacement process to compute various critical exponents governing the large-scale geometry of trees in the forest in a wide variety of “high-dimensional” graphs, including Z^d for d \geq 5 and every bounded degree nonamenable graph. I will then sketch how this allows us to compute related exponents describing the geometry of avalanches in the Abelian sandpile model on the same class of graphs.
Scaling exponents for high-dimensional spanning forests and sandpiles
2018. 05. 17. 16:15
Tom Hutchcroft (Cambridge)