Meaning of peanosphere | Babel Free

Definitions

the scaling limit of random planar maps equipped with a collection of loops coming from a critical FK model.

Examples

“We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the "peano curve" surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a #92;sqrt#123;4#47;3#125;-Liouville quantum gravity surface decorated by an independent Schramm-Loewner evolution with parameter #92;kappa#61;12 (i.e., SLE#95;#123;12#125;).”

CEFR level