Please use this identifier to cite or link to this item: doi:10.22028/D291-34552
Title: Modulus of continuity of controlled Loewner–Kufarev equations and random matrices
Author(s): Amaba, Takafumi
Friedrich, Roland
Language: English
Title: Analysis and Mathematical Physics
Volume: 10
Issue: 2
Publisher/Platform: Springer Nature
Year of Publication: 2020
Free key words: Loewner–Kufarev equation
Witt algebra
Faber polynomia
Grunsky coefficient
Control function
DDC notations: 510 Mathematics
Publikation type: Journal Article
Abstract: First we introduce the two tau-functions which appeared either as the τ -function of the integrable hierarchy governing the Riemann mapping of Jordan curves or in conformal field theory and the universal Grassmannian. Then we discuss various aspects of their interrelation. Subsequently, we establish a novel connection between free probability, growth models and integrable systems, in particular for second order freeness, and summarise it in a dictionary. This extends the previous link between conformal maps and large N-matrix integrals to (higher) order free probability. Within this context of dynamically evolving contours, we determine a class of driving functions for controlled Loewner–Kufarev equations, which enables us to give a continuity estimate for the solution of such an equation when embedded into the Segal–Wilson Grassmannian.
DOI of the first publication: 10.1007/s13324-020-00366-3
Link to this record: urn:nbn:de:bsz:291--ds-345521
ISSN: 1664-235X
Date of registration: 20-Aug-2021
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Professorship: MI - Keiner Professur zugeordnet
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

Files for this record:
File Description SizeFormat 
Amaba-Friedrich2020_Article_ModulusOfContinuityOfControlle.pdf785,96 kBAdobe PDFView/Open

This item is licensed under a Creative Commons License Creative Commons