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Critical percolation in the plane
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We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case we obtain conformal invariance of the crossing probabilities and Cardy's formula. Then we prove existence, uniqueness, and conformal invariance of the continuum scaling limit.
Forward citations
Cited by 3 Pith papers
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On the geometry of locally growing Loewner chains
Loewner chains with local growth admit a generating function η whose left-continuity implies path-connectedness and local connectedness of the hulls.
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Multiple SLEs for $\kappa\in (0,8)$: Coulomb gas integrals and pure partition functions
Constructs SLE(κ) partition functions as Coulomb gas integrals for κ∈(0,8), proves positivity and series properties, builds real-analytic pure partition functions, and relates both via meander matrix to define global ...
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Numerical simulations of the spread from the mean of the SLE and Multiple SLE dynamics
Numerical experiments predict bimodal spread distributions for SLE started near the origin and bell-shaped otherwise, with bell-shaped distributions for multiple SLE in all tested cases.
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