title: Active spanning trees and Schramm-Loewner evolution.
abstract: We consider the Peano curve separating a spanning tree from its dual spanning tree on an embedded planar graph, where the tree and dual tree are weighted by y to the number of active edges, and "active" is in the sense of the Tutte polynomial. When the graph is a portion of the square grid approximating a simply connected domain, it is known (y=1 and y=1+sqrt[2]) or believed (1<y<3) that the Peano curve converges to a space-filling SLE_{κ} loop, where y=1-2cos(4π/κ), corresponding to 4<κ≤8. We argue that the same should hold for 0≤y<1, which corresponds to 8<κ≤12.
authors.affiliation: Departement Mathematik, ETH, 8092 Zürich, Switzerland.
authors.forename: Adrien
authors.initials: A
authors.lastname: Kassel
authors.affiliation: Microsoft Research, Redmond, Washington 98052, USA.
authors.forename: David B
authors.initials: DB
authors.lastname: Wilson