Active spanning trees and SchrammLoewner 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 +√{2 } ) or believed (1 <y <3 ) that the Peano curve converges to a spacefilling S_{L E κ} loop, where y =1 2 cos(4 π /κ ) , corresponding to 4 <κ ≤8 . We argue that the same should hold for 0 ≤y <1 , which corresponds to 8 <κ ≤12 .
 Publication:

Physical Review E
 Pub Date:
 June 2016
 DOI:
 10.1103/PhysRevE.93.062121
 arXiv:
 arXiv:1512.09122
 Bibcode:
 2016PhRvE..93f2121K
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematics  Probability
 EPrint:
 6 pages, 7 figures