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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.06763 |
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| _version_ | 1866909343206604800 |
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| author | Blackstone, Elliot Charlier, Christophe Lenells, Jonatan |
| author_facet | Blackstone, Elliot Charlier, Christophe Lenells, Jonatan |
| contents | We consider Toeplitz determinants whose symbol has: (i) a one-cut regular potential $V$, (ii) Fisher--Hartwig singularities, and (iii) a smooth function in the background. The potential $V$ is associated with an equilibrium measure that is assumed to be supported on the whole unit circle. For constant potentials $V$, the equilibrium measure is the uniform measure on the unit circle and our formulas reduce to well-known results for Toeplitz determinants with Fisher--Hartwig singularities. For non-constant $V$, our results appear to be new even in the case of no Fisher--Hartwig singularities. As applications of our results, we derive various statistical properties of a determinantal point process which generalizes the circular unitary ensemble. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06763 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Toeplitz determinants with a one-cut regular potential and Fisher--Hartwig singularities I. Equilibrium measure supported on the unit circle Blackstone, Elliot Charlier, Christophe Lenells, Jonatan Probability Mathematical Physics We consider Toeplitz determinants whose symbol has: (i) a one-cut regular potential $V$, (ii) Fisher--Hartwig singularities, and (iii) a smooth function in the background. The potential $V$ is associated with an equilibrium measure that is assumed to be supported on the whole unit circle. For constant potentials $V$, the equilibrium measure is the uniform measure on the unit circle and our formulas reduce to well-known results for Toeplitz determinants with Fisher--Hartwig singularities. For non-constant $V$, our results appear to be new even in the case of no Fisher--Hartwig singularities. As applications of our results, we derive various statistical properties of a determinantal point process which generalizes the circular unitary ensemble. |
| title | Toeplitz determinants with a one-cut regular potential and Fisher--Hartwig singularities I. Equilibrium measure supported on the unit circle |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2212.06763 |