Fredholm Determinants from Schrödinger Type Equations, and Deformation of Tracy-Widom Distribution
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913481609969664 |
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| author | Kimura, Taro Navand, Xavier |
| author_facet | Kimura, Taro Navand, Xavier |
| contents | We undertake an analysis of Fredholm determinants arising from kernels whose defining functions satisfy a Schrödinger type equation. When this defining function is the Airy one, the evaluation of the corresponding Fredholm determinant yields the notorious Tracy-Widom distribution [hep-th/9211141], which has found many applications in numerous domains. In this paper, we unveil a generalization of the Tracy-Widom distribution for a generic class of defining functions. Furthermore, we bring forth a direct application of our upshot and survey the relation between the framework which we employ and isomonodromic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06888 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fredholm Determinants from Schrödinger Type Equations, and Deformation of Tracy-Widom Distribution Kimura, Taro Navand, Xavier Mathematical Physics Exactly Solvable and Integrable Systems We undertake an analysis of Fredholm determinants arising from kernels whose defining functions satisfy a Schrödinger type equation. When this defining function is the Airy one, the evaluation of the corresponding Fredholm determinant yields the notorious Tracy-Widom distribution [hep-th/9211141], which has found many applications in numerous domains. In this paper, we unveil a generalization of the Tracy-Widom distribution for a generic class of defining functions. Furthermore, we bring forth a direct application of our upshot and survey the relation between the framework which we employ and isomonodromic systems. |
| title | Fredholm Determinants from Schrödinger Type Equations, and Deformation of Tracy-Widom Distribution |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2408.06888 |