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The strange geometry of highdimensional random spanning forestsSeminar: Probability Seminar  March 22  3:104 p.m.  1011 Evans Hall Yuval Peres, Microsoft Research 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.) 5106422781 

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