Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants
This work provides the general framework for obtaining strong Szegő limit theorems for multi-bordered, semi-framed, framed, and multi-framed Toeplitz determinants, extending the results of Basor et al. (2022) beyond the (single) bordered Toeplitz case. For the two-bordered and also the semi-framed T...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2024 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212358 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants. Roozbeh Gharakhloo. SIGMA 20 (2024), 062, 51 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862536410548928512 |
|---|---|
| author | Gharakhloo, Roozbeh |
| author_facet | Gharakhloo, Roozbeh |
| citation_txt | Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants. Roozbeh Gharakhloo. SIGMA 20 (2024), 062, 51 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This work provides the general framework for obtaining strong Szegő limit theorems for multi-bordered, semi-framed, framed, and multi-framed Toeplitz determinants, extending the results of Basor et al. (2022) beyond the (single) bordered Toeplitz case. For the two-bordered and also the semi-framed Toeplitz determinants, we compute the strong Szegő limit theorems associated with certain classes of symbols, and for the -bordered ( ≥ 3), framed, and multi-framed Toeplitz determinants, we demonstrate the recursive fashion offered by the Dodgson condensation identities via which strong Szegő limit theorems can be obtained. One instance of the appearance of semi-framed Toeplitz determinants is in calculations related to the entanglement entropy for disjoint subsystems in the XX spin chain (Brightmore et al. (2020) and Jin-Korepin (2011)). In addition, in the recent work of Gharakhloo and Liechty (2024) and in an unpublished work of Professor Nicholas Witte, such determinants have found relevance respectively in the study of ensembles of nonintersecting paths and in the study of off-diagonal correlations of the anisotropic square-lattice Ising model. Besides the intrinsic mathematical interest in these structured determinants, the aforementioned applications have further motivated the study of the present work.
|
| first_indexed | 2026-03-12T16:33:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212358 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T16:33:48Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gharakhloo, Roozbeh 2026-02-05T09:56:37Z 2024 Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants. Roozbeh Gharakhloo. SIGMA 20 (2024), 062, 51 pages 1815-0659 2020 Mathematics Subject Classification: 15B05;30E15;30E25 arXiv:2309.14695 https://nasplib.isofts.kiev.ua/handle/123456789/212358 https://doi.org/10.3842/SIGMA.2024.062 This work provides the general framework for obtaining strong Szegő limit theorems for multi-bordered, semi-framed, framed, and multi-framed Toeplitz determinants, extending the results of Basor et al. (2022) beyond the (single) bordered Toeplitz case. For the two-bordered and also the semi-framed Toeplitz determinants, we compute the strong Szegő limit theorems associated with certain classes of symbols, and for the -bordered ( ≥ 3), framed, and multi-framed Toeplitz determinants, we demonstrate the recursive fashion offered by the Dodgson condensation identities via which strong Szegő limit theorems can be obtained. One instance of the appearance of semi-framed Toeplitz determinants is in calculations related to the entanglement entropy for disjoint subsystems in the XX spin chain (Brightmore et al. (2020) and Jin-Korepin (2011)). In addition, in the recent work of Gharakhloo and Liechty (2024) and in an unpublished work of Professor Nicholas Witte, such determinants have found relevance respectively in the study of ensembles of nonintersecting paths and in the study of off-diagonal correlations of the anisotropic square-lattice Ising model. Besides the intrinsic mathematical interest in these structured determinants, the aforementioned applications have further motivated the study of the present work. The author would like to thank Harini Desiraju, Alexander Its, Karl Liechty, and Nicholas Witte for their interest in this Project and for helpful conversations. The author would also like to thank the anonymous referees for their helpful remarks andsuggestions. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1928930. The author gratefully acknowledges the Mathematical Sciences Research Institute, Berkeley, California, and the organizers of the semester-long program Universality and Integrability in Random Matrix Theory and Interacting Particle Systems for their support in the Fall of 2021, during which part of this Project was completed. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants Article published earlier |
| spellingShingle | Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants Gharakhloo, Roozbeh |
| title | Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants |
| title_full | Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants |
| title_fullStr | Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants |
| title_full_unstemmed | Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants |
| title_short | Strong Szegő Limit Theorems for Multi-Bordered, Framed, and Multi-Framed Toeplitz Determinants |
| title_sort | strong szegő limit theorems for multi-bordered, framed, and multi-framed toeplitz determinants |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212358 |
| work_keys_str_mv | AT gharakhlooroozbeh strongszegolimittheoremsformultiborderedframedandmultiframedtoeplitzdeterminants |