peanosphere

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noun

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

Scrabble 18
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Meanings

nounpeanosphere (plural peanospheres)

plural peanospheres

  1. mathematicsthe scaling limit of random planar maps equipped with a collection of loops coming from a critical FK model.
    1 more example

    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

Origin

From Peano + -sphere.

Full word history & related roots →
Cite this entry
APA

peanosphere. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/peanosphere

MLA

“peanosphere.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/peanosphere. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “peanosphere,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/peanosphere.

Source: peanosphere on Wiktionary, CC BY-SA 4.0.