A tree-weighted planar map is a random planar map whose probability is proportional
to its number of spanning trees. Equivalently, sample
uniformly a pair 
consisting of a rooted spherical map with a prescribed
number of edges and a distinguished spanning
tree. Conditional on 
, the tree 
is uniform among its spanning
trees. The graph distance and corner probability
measure use the full map, including edges outside
.
Tree-Weighted Planar Map
See also
Liouville Quantum Sphere, Random Planar Map, Spanning TreeExplore with Wolfram|Alpha
References
Sheffield, S. "Quantum Gravity and Inventory Accumulation." Ann. Probab. 44, 3804-3848, 2016. https://doi.org/10.1214/15-AOP1061.Cite this as:
Weisstein, Eric W. "Tree-Weighted Planar Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Tree-WeightedPlanarMap.html