Percolation and $O(1)$ loop model

Mikhail Khristoforov; Stanislav Smirnov

Percolation and $O(1)$ loop model

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arxiv 2111.15612 v1 pith:FROTKTGO submitted 2021-11-30 math.PR math-phmath.CVmath.MP

Mikhail Khristoforov , Stanislav Smirnov This is my paper · ORCID

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keywords percolationamenableapproachcardyciteconceptualconformallycritical

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We present an "ultimate" proof of Cardy's formula for the critical percolation on the hexagonal lattice \cite{Smirnov01criticalpercolation}, showing the existence of the universal and conformally invariant scaling limit of crossing probabilities. The new approach is more conceptual, less technically demanding, and is amenable to generalizations.

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On loops in the complement to dimers
math.PR 2024-12 reject novelty 7.0 of 10

For every non-frozen translation-invariant ergodic Gibbs measure of the loop O(1) model at x=8 on the hexagonal lattice, the complement to the dimer configuration has either infinitely many loops around every face or ...

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