Dictionary

peanosphere en · NOUN

Etymology

From Peano + -sphere.

Meanings

1. the scaling limit of random planar maps equipped with a collection of loops coming from a critical FK model.
   • 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;). 2015, Richard Kenyon, Jason Miller, Scott Sheffield, David B. Wilson, “Bipolar orientations on planar maps and SLE₁₂”, in arXiv:

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