Crossing Probabilities of Multiple Ising Interfaces

Abstract

We prove that in the scaling limit, the crossing probabilities of multiple interfaces in the critical planar Ising model with alternating boundary conditions are conformally invariant expressions given by the pure partition functions of multiple SLE(κ) with κ=3. In particular, this identifies the scaling limits with ratios of specific correlation functions of conformal field theory.

35 pages, 2 figures; v4(final) to appear in Ann. Appl. Probab

References in corpus (7)

• The scaling limits of planar LERW in finitely connected domains
• Global and Local Multiple SLEs for $\kappa \le 4$ and Connection Probabilities for Level Lines of GFF
• Smirnov's observable for free boundary conditions, interfaces and crossing probabilities
• A solution space for a system of null-state partial differential equations 4
• Towards a conformal field theory for Schramm-Loewner evolutions
• Boundary correlations in planar LERW and UST
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Cited by in corpus (4)

• Connection Probabilities of Multiple FK-Ising Interfaces
• Uniform Spanning Tree in Topological Polygons, Partition Functions for SLE(8), and Correlations in $c=-2$ Logarithmic CFT
• Multiple Ising interfaces in annulus and $2N$-sided radial SLE
• Planar UST Branches and $c=-2$ Degenerate Boundary Correlations