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The strange geometry of high-dimensional random spanning forests

Seminar: Probability Seminar | March 22 | 3:10-4 p.m. | 1011 Evans Hall

Yuval Peres, Microsoft Research

Department of Statistics

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 every time the dimension increases by 1. (Joint work with Tom Hutchcroft.)