peanosphere

peanosphere

English

Etymology

peano- +‎ sphere

Noun

peanosphere

1. (mathematics) the scaling limit of random planar maps equipped with a collection of loops coming from a critical FK model.
   • 2015, Richard Kenyon, Jason Miller, Scott Sheffield, David B. Wilson, “Bipolar orientations on planar maps and SLE${\\displaystyle _{12}}$”, in arXiv‎:

     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 ${\\displaystyle {\\sqrt {4/3}}}$-Liouville quantum gravity surface decorated by an independent Schramm-Loewner evolution with parameter ${\\displaystyle \\kappa =12}$ (i.e., SLE${\\displaystyle _{12}}$).