Conformally covariant probabilities, operator product expansions, and logarithmic correlations in two-dimensional critical percolation
The large-scale behavior of two-dimensional critical percolation is expected to be described
by a conformal field theory (CFT). Moreover, this putative percolation CFT is believed to be …
by a conformal field theory (CFT). Moreover, this putative percolation CFT is believed to be …
Compactified Imaginary Liouville Theory
C Guillarmou, A Kupiainen, R Rhodes - arXiv preprint arXiv:2310.18226, 2023 - arxiv.org
On a given Riemann surface, we construct a path integral based on the Liouville action
functional with imaginary parameters. The construction relies on the compactified Gaussian …
functional with imaginary parameters. The construction relies on the compactified Gaussian …
Planar UST Branches and Degenerate Boundary Correlations
A Karrila, A Lafay, E Peltola, J Roussillon - arXiv preprint arXiv …, 2024 - arxiv.org
We provide a conformal field theory (CFT) description of the probabilistic model of boundary
effects in the wired uniform spanning tree (UST) and its algebraic content, concerning the …
effects in the wired uniform spanning tree (UST) and its algebraic content, concerning the …
Connection probabilities of multiple FK-Ising interfaces
We find the scaling limits of a general class of boundary-to-boundary connection
probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying …
probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying …
Conformal covariance of connection probabilities and fields in 2D critical percolation
F Camia - Communications on Pure and Applied Mathematics, 2024 - Wiley Online Library
Fitting percolation into the conformal field theory framework requires showing that
connection probabilities have a conformally invariant scaling limit. For critical site …
connection probabilities have a conformally invariant scaling limit. For critical site …
Crossing probabilities of multiple Ising interfaces
E Peltola, H Wu - arXiv preprint arXiv:1808.09438, 2018 - arxiv.org
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 …
critical planar Ising model with alternating boundary conditions are conformally invariant …
Radial BPZ equations and partition functions of FK-Ising interfaces conditional on one-arm event
Radial BPZ equations come naturally when one solves Dub\'{e} dat's commutation relation
in the radial setting. We construct positive solutions to radial BPZ equations and show that …
in the radial setting. We construct positive solutions to radial BPZ equations and show that …
Hypergeometric SLE with : Convergence of UST and LERW in Topological Rectangles
Y Han, M Liu, H Wu - arXiv preprint arXiv:2008.00403, 2020 - arxiv.org
We consider uniform spanning tree (UST) in topological rectangles with alternating
boundary conditions. The Peano curves associated to the UST converge weakly to …
boundary conditions. The Peano curves associated to the UST converge weakly to …
Symplectic fermions in general domains
D Adame-Carrillo - arXiv preprint arXiv:2409.12823, 2024 - arxiv.org
In this note, we construct a logarithmic conformal field theory in general domains of the
complex plane. The theory of interest is the symplectic fermions because of its links to …
complex plane. The theory of interest is the symplectic fermions because of its links to …
Loop-erased random walk branch of uniform spanning tree in topological polygons
M Liu, H Wu - Bernoulli, 2023 - projecteuclid.org
We consider uniform spanning tree (UST) in topological polygons with 2 N marked points on
the boundary with alternating boundary conditions. In an earlier work by Liu-Peltola-Wu, the …
the boundary with alternating boundary conditions. In an earlier work by Liu-Peltola-Wu, the …