5 papers
Level lines of the Gaussian free field and degenerate conformal blocks
Alex Karrila, Eveliina Peltola, Lukas Schoug
We consider Gaussian free field (GFF) on simply connected domains with piecewise constant Dirichlet boundary data. We show that the crossing probabilities for its level lines are d…
Smoothness of martingale observables and generalized Feynman-Kac formulas
Alex Karrila, Lauri Viitasaari
We prove that, under the Hörmander criterion on an Itô process, all its martingale observables are smooth. As a consequence, we also obtain a generalized Feynman-Kac formula prov…
A new computation of pairing probabilities in several multiple-curve models
Alex Karrila
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 Ga…
Planar UST Branches and Degenerate Boundary Correlations
Alex Karrila, Augustin Lafay, Eveliina Peltola +1
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…
Operator product expansions of derivative fields in the sine-Gordon model
Alex Karrila, Tuomas Virtanen, Christian Webb
In this article, we initiate the study of operator product expansions (OPEs) for the sine-Gordon model. For simplicity, we focus on the model below the first threshold of collapse…