- Working Paper
We study random two-dimensional spanning forests in the plane that can be viewed both in the discrete case and in their scaling limit as slight perturbations of an uniformly chosen spanning tree. We show how to relate this scaling limit to a stationary distribution of a natural Markov process on a state of abstract graphs with non-constant edge-weights. This simple Markov process can be viewed as a renormalization flow, so that in this two-dimensional case, one can give a rigorous meaning to the fact that there is a unique fixed point (ie. stationary distribution) in two dimensions for this renormalization flow, and that when starting from any periodic two-dimensional lattice, the renormalization flow converges to this fixed point (ie. the Markov process converges in law to its stationary distribution).<br/> While the results of this paper are dealing with the planar case and build on the convergence in distribution of branches of the UST to SLE2 as well as on the predicted convergence of the suitably renormalized length of the loop-erased random walk to the "natural parametrization" of the SLE2, this Markov process setup is in fact not restricted to two dimensions Show more
Journal / seriesarXiv
Pages / Article No.
Organisational unit09453 - Werner, Wendelin / Werner, Wendelin
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