On Airy solutions of P$_\mathrm{II}$ and the complex cubic ensemble of random matrices, II
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910355873071104 |
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| author | Barhoumi, Ahmad Bleher, Pavel Deaño, Alfredo Yattselev, Maxim L. |
| author_facet | Barhoumi, Ahmad Bleher, Pavel Deaño, Alfredo Yattselev, Maxim L. |
| contents | We describe the pole-free regions of the one-parameter family of special solutions of P$_\mathrm{II}$, the second Painlevé equation, constructed from the Airy functions. This is achieved by exploiting the connection between these solutions and the recurrence coefficients of orthogonal polynomials that appear in the analysis of the ensemble of random matrices corresponding to the cubic potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Airy solutions of P$_\mathrm{II}$ and the complex cubic ensemble of random matrices, II Barhoumi, Ahmad Bleher, Pavel Deaño, Alfredo Yattselev, Maxim L. Mathematical Physics Classical Analysis and ODEs 15B52, 33C10, 33C47 We describe the pole-free regions of the one-parameter family of special solutions of P$_\mathrm{II}$, the second Painlevé equation, constructed from the Airy functions. This is achieved by exploiting the connection between these solutions and the recurrence coefficients of orthogonal polynomials that appear in the analysis of the ensemble of random matrices corresponding to the cubic potential. |
| title | On Airy solutions of P$_\mathrm{II}$ and the complex cubic ensemble of random matrices, II |
| topic | Mathematical Physics Classical Analysis and ODEs 15B52, 33C10, 33C47 |
| url | https://arxiv.org/abs/2403.03023 |