The strange geometry of high-dimensional random spanning forests

Probability Seminar
Mar 22, 2017 3:10pm to 4:00pm
1011 Evans Hall
Happening As Scheduled
The uniform spanning forest (USF) in the lattice Z^d, first studied by Pemantle (Ann. Prob. 1991) following a suggestion of R. Lyons, is defined as a limit of uniform spanning trees in growing finite boxes. Although the USF is a limit of trees, it might not be connected- Indeed, Pemantle proved that the USF in Z^d is connected if and only if d8 the USF geometry undergoes a qualitative change...
Yuval Peres, Microsoft Research