18 citations · 80 across the 15 of their papers we have counts for
18 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 provid…
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…
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…
Logarithmic delocalization of random Lipschitz functions on honeycomb and other lattices
Alex M. Karrila
We study random one-Lipschitz integer functions on the vertices of a finite connected graph, sampled according to the weight $W(f) = \prod_{\langle v, w \rangle \in E} \mathbf{…
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…
Delocalization of the height function of the six-vertex model
Hugo Duminil-Copin, Alex Karrila, Ioan Manolescu +1
We show that the height function of the six-vertex model, in the parameter range and , is delocalized with logarithmic variance when $\mathbf…
UST branches, martingales, and multiple SLE(2)
Alex Karrila
We identify the local scaling limit of multiple boundary-to-boundary branches in a uniform spanning tree (UST) as a local multiple SLE(2), i.e., an SLE(2) process weighted by a sui…
Multiple SLE type scaling limits: from local to global
Alex Karrila
We consider collections of chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected d…
Limits of conformal images and conformal images of limits for planar random curves
Alex M. Karrila
We address the scaling limits of random curves arising from, e.g., planar lattice models, especially in rough domains. The well-known precompactness conditions of Kemppainen and Sm…
Conformal blocks, -combinatorics, and quantum group symmetry
Alex Karrila, Kalle Kytölä, Eveliina Peltola
In this article, we find a -analogue for Fomin's formulas. The original Fomin's formulas relate determinants of random walk excursion kernels to loop-erased random walk partitio…
Boundary correlations in planar LERW and UST
Alex Karrila, Kalle Kytölä, Eveliina Peltola
We find explicit formulas for the probabilities of general boundary visit events for planar loop-erased random walks, as well as connectivity events for branches in the uniform spa…
Lattice coding for Rician fading channels from Hadamard rotations
Alex Karrila, Niko R. Väisänen, David Karpuk +1
In this paper, we study lattice coding for Rician fading wireless channels. This is motivated in particular by preliminary studies suggesting the Rician fading model for millimeter…
Well-Rounded Lattices for Coset Coding in MIMO Wiretap Channels
Oliver W. Gnilke, Amaro Barreal, Alex Karrila +3
The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that,…
Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels
Mohamed Taoufiq Damir, Alex Karrila, Laia Amorós +3
The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From th…
Information Bounds and Flatness Factor Approximation for Fading Wiretap MIMO Channels
Amaro Barreal, Alex Karrila, David Karpuk +1
In this article, the design of secure lattice coset codes for general wireless channels with fading and Gaussian noise is studied. Recalling the eavesdropper's probability and info…
Well-Rounded Lattices for Reliability and Security in Rayleigh Fading SISO Channels
Oliver Wilhelm Gnilke, Ha Thanh Nguyen Tran, Alex Karrila +1
For many wiretap channel models asymptotically optimal coding schemes are known, but less effort has been put into actual realizations of wiretap codes for practical parameters. Bo…
A Comparison of Skewed and Orthogonal Lattices in Gaussian Wiretap Channels
Alex Karrila, Camilla Hollanti
We consider lattice coset-coded transmissions over a wiretap channel with additive white Gaussian noise (AWGN). Examining a function that can be interpreted as either the legitimat…