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Modulus of continuity of controlled Loewner–Kufarev equations and random matrices
First we introduce the two tau-functions which appeared either as the [Formula: see text] -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. Subseque...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer International Publishing
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550653/ https://www.ncbi.nlm.nih.gov/pubmed/34777237 http://dx.doi.org/10.1007/s13324-020-00366-3 |
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author | Amaba, Takafumi Friedrich, Roland |
author_facet | Amaba, Takafumi Friedrich, Roland |
author_sort | Amaba, Takafumi |
collection | PubMed |
description | First we introduce the two tau-functions which appeared either as the [Formula: see text] -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. |
format | Online Article Text |
id | pubmed-8550653 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-85506532021-11-10 Modulus of continuity of controlled Loewner–Kufarev equations and random matrices Amaba, Takafumi Friedrich, Roland Anal Math Phys Article First we introduce the two tau-functions which appeared either as the [Formula: see text] -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. Springer International Publishing 2020-05-08 2020 /pmc/articles/PMC8550653/ /pubmed/34777237 http://dx.doi.org/10.1007/s13324-020-00366-3 Text en © The Author(s) 2021, corrected publication 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Amaba, Takafumi Friedrich, Roland Modulus of continuity of controlled Loewner–Kufarev equations and random matrices |
title | Modulus of continuity of controlled Loewner–Kufarev equations and random matrices |
title_full | Modulus of continuity of controlled Loewner–Kufarev equations and random matrices |
title_fullStr | Modulus of continuity of controlled Loewner–Kufarev equations and random matrices |
title_full_unstemmed | Modulus of continuity of controlled Loewner–Kufarev equations and random matrices |
title_short | Modulus of continuity of controlled Loewner–Kufarev equations and random matrices |
title_sort | modulus of continuity of controlled loewner–kufarev equations and random matrices |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550653/ https://www.ncbi.nlm.nih.gov/pubmed/34777237 http://dx.doi.org/10.1007/s13324-020-00366-3 |
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