Massive CLE2 boundary conjecture for the canonical evaporated UST component
Massive CLE2 boundary conjecture for the canonical evaporated UST component
Condition on the event , and let be the canonical embedding of the root component obtained by edge evaporation. The massive boundary conjecture. The rescaled vertex sets
converge in distribution for the Hausdorff metric on compact subsets of to a limiting compact set with Lebesgue measure that is simply connected, and the boundary of is a massive version of conditioned to have area . This is a conjectural description of the continuum boundary of the conditioned evaporated-tree shape; the source gives no proof or resolution.
Sources & referencesView supporting material
Primary source
Luis Fredes and Jean-Francois Marckert, “Models of random subtrees of a graph”, arXiv:2102.12738 (2023).
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