Coupling of Gaussian free fields and Schramm--Loewner evolutions on multiply connected domains

Project Details


This project is concerned with the mathematical understanding of critical systems in two dimensions, in particular, in the case that systems live on multiply connected domains. As a specific example of such a critical system, we concentrate on a model called Gaussian free field (GFF). A central issue under this setting is to determine the probability law of the random curve associated to the GFF typically as the contour line, or the flow line of a vector field defined in terms of the GFF. In this project, we especially consider the case that candidates for such random curves are given by an annulus Schramm-Loewner evolution or a Komatu-Loewner evolution and intend to prove that these candidates are indeed flow lines of GFFs. The anticipated results will be a significant step towards the full understanding of the conformal invariance of critical systems. This project is carried out at Department of Mathematics and Systems Analysis, Aalto University.
AcronymKoshida Shinji
Effective start/end date01/09/202131/08/2024


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