Transition Analysis: From the Airy and Pearcey Kernels to the Sine Kernel
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912156181594112 |
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| author | Neuschel, Thorsten Venker, Martin |
| author_facet | Neuschel, Thorsten Venker, Martin |
| contents | We study transitions between the three universal limiting kernels Airy, Pearcey and sine kernel, arising in Random Matrix Theory at edge, cusp and bulk points of the spectrum. Under appropriate rescalings, we provide complete asymptotic expansions of the extended Airy kernel and the extended Pearcey kernel approaching the extended sine kernel, expliciting the fluctuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transition Analysis: From the Airy and Pearcey Kernels to the Sine Kernel Neuschel, Thorsten Venker, Martin Classical Analysis and ODEs Mathematical Physics Probability 60B20, 41A60 We study transitions between the three universal limiting kernels Airy, Pearcey and sine kernel, arising in Random Matrix Theory at edge, cusp and bulk points of the spectrum. Under appropriate rescalings, we provide complete asymptotic expansions of the extended Airy kernel and the extended Pearcey kernel approaching the extended sine kernel, expliciting the fluctuations. |
| title | Transition Analysis: From the Airy and Pearcey Kernels to the Sine Kernel |
| topic | Classical Analysis and ODEs Mathematical Physics Probability 60B20, 41A60 |
| url | https://arxiv.org/abs/2412.10596 |