A1189
Title: Covariance and autocovariance estimation on a Liouville quantum gravity sphere in a functional context
Authors: Andrej Srakar - Institute for Economic Research Ljubljana (Slovenia) [presenting]
Abstract: Research on spherical random fields and their applications has become an important part of probability, statistics and mathematical physics. Approaches are extended to study anisotropic spherical random fields previously unaddressed in this context area in random geometry, namely Liouville quantum gravity (LQG) spheres. The quantum Liouville theory was introduced in 1981 as a model for quantizing the bosonic string in the conformal gauge and gravity in two space-time dimensions. Liouville measure is formally the exponential of the Gaussian free field (GFF), and it is possible to study in depth its properties about SLE curves or geometrical objects in the plane that can be constructed out of the GFF. The problem of estimation of Green-type covariance is studied, and autocovariance functions of a continuous Gaussian free field are defined on an LQG sphere. Their estimators are proposed within a functional data analysis context and study their asymptotics, including their computational aspects. In an application, data on sea surface temperature anomalies (temperature and salinity of the upper 2000 m of the ocean) is studied and recorded by Argo floats. In conclusion, extensions are discussed in many areas of studying spherical random fields and their relationship to probability and random geometry in a functional context.
