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Decomposition of global 2-SLE for kappain (4,8) and an application for critical FK-Ising model
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Decomposition of global 2-SLE for $\kappa\in (4,8)$ and an application for critical FK-Ising model
abstract
We consider global 2-SLE$_{\kappa}$ $(\eta_1, \eta_2)$ in a topological rectangle with $\kappa\in (4,8)$. We derive the law of a random hitting point of the curves and show that, conditional on this random hitting point, the pair of two curves has the same law as Gaussian free field flow lines with proper boundary data. Using a similar idea, we derive the asymptotic of the probability for $\eta_1\cap\eta_2=\emptyset$. As an application, we derive the asymptotic of the probability for the existence of two disjoint open paths in critical FK-Ising model.
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Cited by 1 Pith paper
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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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