Abstract.
Double-scaling limits of Toeplitz determinants Dn(ft) generated by a set of functions ft ∈ L1 are discussed as both n → ∞ and t → 0 simultaneously, which is currently of great importance in mathematics and in physics. The main focus is on the cases where the number of Fisher–Hartwig singularities changes as t → 0. All the results on double-scaling limits are discussed in the context of applications in random matrix theory and in mathematical physics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Virtanen, J.A. (2018). Double-scaling limits of Toeplitz determinants and Fisher–Hartwig singularities. In: Böttcher, A., Potts, D., Stollmann, P., Wenzel, D. (eds) The Diversity and Beauty of Applied Operator Theory. Operator Theory: Advances and Applications, vol 268. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-75996-8_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-75996-8_29
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-75995-1
Online ISBN: 978-3-319-75996-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)