Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity
We study n×n Hankel determinants constructed with moments of a Hermite weight with a Fisher-Hartwig singularity on the real line. We consider the case when the singularity is in the bulk and is both of root-type and jump-type. We obtain large n asymptotics for these Hankel determinants, and we obser...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209446 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity / C. Charlier, A. Deaño // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 41 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862636071453458432 |
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| author | Charlier, C. Deaño, A. |
| author_facet | Charlier, C. Deaño, A. |
| citation_txt | Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity / C. Charlier, A. Deaño // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study n×n Hankel determinants constructed with moments of a Hermite weight with a Fisher-Hartwig singularity on the real line. We consider the case when the singularity is in the bulk and is both of root-type and jump-type. We obtain large n asymptotics for these Hankel determinants, and we observe a critical transition when the size of the jumps varies with n. These determinants arise in the thinning of the generalised Gaussian unitary ensembles and in the construction of special function solutions of the Painlevé IV equation.
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| first_indexed | 2025-11-30T21:24:59Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209446 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T21:24:59Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Charlier, C. Deaño, A. 2025-11-21T18:59:52Z 2018 Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity / C. Charlier, A. Deaño // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 41 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 30E15; 35Q15; 15B52; 33E17 arXiv: 1708.02519 https://nasplib.isofts.kiev.ua/handle/123456789/209446 https://doi.org/10.3842/SIGMA.2018.018 We study n×n Hankel determinants constructed with moments of a Hermite weight with a Fisher-Hartwig singularity on the real line. We consider the case when the singularity is in the bulk and is both of root-type and jump-type. We obtain large n asymptotics for these Hankel determinants, and we observe a critical transition when the size of the jumps varies with n. These determinants arise in the thinning of the generalised Gaussian unitary ensembles and in the construction of special function solutions of the Painlevé IV equation. C. Charlier was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007/2013)/ ERC Grant Agreement n. 307074. A. Deaño acknowledges financial support from projects MTM2012-36732-C03-01 and MTM2015-65888-C4-2-P from the Spanish Ministry of Economy and Competitiveness. The authors are grateful to A.B.J. Kuijlaars for sharing a simplified proof for the first part of [11, Proposition A.1]. This inspired us to simplify the proof of Lemma 7.4. We also thank T. Claeys for a careful reading of the introduction and for useful remarks. The authors acknowledge the referees for their careful reading and useful remarks. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity Article published earlier |
| spellingShingle | Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity Charlier, C. Deaño, A. |
| title | Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity |
| title_full | Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity |
| title_fullStr | Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity |
| title_full_unstemmed | Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity |
| title_short | Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity |
| title_sort | asymptotics for hankel determinants associated to a hermite weight with a varying discontinuity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209446 |
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