3. nóvember, kl. 11:40
Stofa 152 í VR-2
Fyrirlesari: Adam Timar
Titill: On Uniform Spanning Forests
Ágrip: How can we generate a random labyrinth efficiently, and how can we describe its properties, such as the expected distance between two points in the labyrinth? This question can be made precise and answered through the study of Uniform Spanning Trees. Given a finite graph, a uniformly chosen random spanning tree is called the Uniform Spanning Tree. It has an analogue on infinite graphs, called the Uniform Spanning Forest (USF). The study of the USF on planar lattices played a crucial role in understanding scaling limits of 2 dimensional statistical physics models. On other transitive graphs the properties of the USF are connected to delicate geometric properties of the graph. I will speak about some related recent joint work with G. Pete.
The talk is meant to be accessible without any background knowledge.