SLE boundary visits
type: Item
instance of: scholarly article
title: SLE boundary visits
zbMATH Open document ID: 1346.82012
author: Niko Jokela
author: Matti Järvinen
author: Kalle Kytölä
published in: Annales Henri Poincaré
publication date: 2016-06-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1311.2297
review text: The present paper deals with the probabilities with which chordal Schramm-Loewner evolutions (SLE) visit small neighborhoods of boundary points. The authors employ a method based on quantum group calculations which allow them to explicitly calculate solutions of the chordal SLE\(_k\) boundary visit probability amplitudes. The solutions are expressed in terms of linear combinations of Coulomb gas integrals and can be transformed into regularized real integrals. Here, the authors also use the technique of a spin chain-Coulomb gas correspondence between tensor product representations of a quantum group and functions given by Dotsenko-Fateev type integrals. In particular, the obtained formulas are applied to the renormalized scaling limit boundary visit probabilities for lattice model interfaces. The results are compared with numerical simulations of percolation, loop-erased random walks, and Fortuin-Kasteleyn random cluster models.
reviewed by: Farruh Mukhamedov
Mathematics Subject Classification ID: 82B24
Mathematics Subject Classification ID: 82C24
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 60J67
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 6592861
zbMATH Keywords: chordal
zbMATH Keywords: Schramm-Loewner evolutions
zbMATH Keywords: probability amplitudes
zbMATH Keywords: quantum group
MaRDI profile type: Publication
OpenAlex ID: W2963765799
arXiv ID: 1311.2297
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DOI: 10.1007/S00023-015-0452-7
description: scientific article; zbMATH DE number 6592861