Active Spanning Trees with Bending Energy on Planar Maps and SLE-Decorated Liouville Quantum Gravity for

作者：Gwynne Ewain^*; Kassel Adrien; Miller Jason; Wilson David B

来源：Communications in Mathematical Physics, 2018, 358(3): 1065-1115.

DOI：10.1007/s00220-018-3104-1

We introduce a two-parameter family of probability measures on spanning trees of a planar map. One of the parameters controls the activity of the spanning tree and the other is a measure of its bending energy. When the bending parameter is 1, we recover the active spanning tree model, which is closely related to the critical Fortuin-Kasteleyn model. A random planar map decorated by a spanning tree sampled from our model can be encoded by means of a generalized version of Sheffield's hamburger-cheeseburger bijection. Using this encoding, we prove that for a range of parameter values (including the ones corresponding to maps decorated by an active spanning tree), the infinite-volume limit of spanning-tree-decorated planar maps sampled from our model converges in the peanosphere sense, upon rescaling, to an -decorated gamma-Liouville quantum cone with and .kappa > 8 and gamma = 4/root kappa (0, root 2).

• 出版日期2018-3
• 单位MIT; Microsoft