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We give a new, short computation of pairing probabilities for multiple chordal interfaces in the critical Ising model, the harmonic explorer, and for multiple level lines of the Gaussian free field.
The Maximum Principle for Biharmonic Functions
R. J. Duffin · 1961
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Scaling limits of loop-erased random walks and uniform spanning trees
O. Schramm · 2000
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Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits
S. Smirnov · 2001
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Conformal invariance of planar loop-erased random walks and uniform spanning trees
G. F. Lawler, O. Schramm, and W. Werner · 2004
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Multiple Schramm–Loewner evolutions and statistical mechanics martingales
M. Bauer, D. Bernard, and K. Kytölä · 2005
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Conformally invariant processes in the plane
G. F. Lawler · 2005
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Basic properties of 𝖲𝖫𝖤 \mathsf{SLE}
S. Rohde and O. Schramm · 2005
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Harmonic explorer and its convergence to 𝖲𝖫𝖤 4 \mathsf{SLE}_{4}
O. Schramm and S. Sheffield · 2005
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Euler integrals for commuting SLEs
J. Dubédat · 2006
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The Malliavin calculus and related topics
D. Nualart · 2006
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Commutation relations for SLE
— · 2007
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Contour lines of the two-dimensional discrete Gaussian free field
— · 2009
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Discrete complex analysis on isoradial graphs
D. Chelkak and S. Smirnov · 2011
Cited alongside, same era.
Boundary partitions in trees and dimers
R. W. Kenyon and D. B. Wilson · 2011
Cited alongside, same era.
Convergence of Ising interfaces to Schramm’s SLE curves
D. Chelkak, H. Duminil-Copin, C. Hongler, A. Kemppainen, and S. Smirnov · 2014
Cited alongside, same era.
A solution space for a system of null-state partial differential equations, Part I
S. M. Flores and P. Kleban · 2015
Cited alongside, same era.
A solution space for a system of null-state partial differential equations, Part II
— · 2015
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A solution space for a system of null-state partial differential equations, Part III
— · 2015
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Preprint, https://arxiv.org/abs/1903.10354 , 2019
A. Karrila. Multiple SLE type scaling limits: from local to global · 2019
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Towards a conformal field theory for Schramm-Loewner evolutions
E. Peltola · 2019
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Global and Local Multiple SLEs for κ ≤ 4 \kappa\leq 4 and Connection Probabilities for Level Lines of GFF
E. Peltola and H. Wu · 2019
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Electr. J. Probab. 25, 2020
—. UST branches, martingales, and multiple SLE(2) · 2020
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Boundary correlations in planar LERW and UST
A. Karrila, K. Kytölä, and E. Peltola · 2020
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On the Uniqueness of Global Multiple SLEs
V. Beffara, E. Peltola, and H. Wu · 2021
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A solution space for a system of null-state partial differential equations, Part IV
— · 2015
Cited alongside, same era.
Crossing probabilities in topological rectangles for the critical planar FK-Ising model
D. Chelkak, H. Duminil-Copin, and C. Hongler · 2016
Cited alongside, same era.
Pure partition functions of multiple SLEs
K. Kytölä and E. Peltola · 2016
Cited alongside, same era.
Imaginary geometry I: interacting SLEs
J. Miller and S. Sheffield · 2016
Cited alongside, same era.
Critical Ising interfaces in multiply-connected domains
K. Izyurov · 2017
Cited alongside, same era.
Random curves, scaling limits, and Loewner evolutions
A. Kemppainen and S. Smirnov · 2017
Cited alongside, same era.
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Scaling limits of crossing probabilities in metric graph GFF
M. Liu and H. Wu · 2021
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Lecture notes on the Gaussian free field
W. Werner and E. Powell · 2022
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Crossing Probabilities of Multiple Ising Interfaces
— · 2023
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Connection Probabilities of Multiple FK-Ising Interfaces
Y. Feng, E. Peltola, and H. Wu · 2024
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Planar UST branches and c = − 2 c=-2 degenerate boundary correlations
A. Karrila, A. Lafay, E. Peltola, and J. Roussillon · 2025
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