Large-Parameter Asymptotics of Generalized Hasting-McLeod Functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913311184912384 |
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| author | Schmidt, Kurt Buckingham, Robert |
| author_facet | Schmidt, Kurt Buckingham, Robert |
| contents | The generalized Hastings-McLeod solutions to the inhomogeneous Painlevé-II equation arise in multi-critical unitary random matrix ensembles, the chiral two-matrix model for rectangular matrices, non-intersecting squared Bessel paths, and non-intersecting Brownian motions on the circle. We establish the leading-order asymptotic behavior of the generalized Hastings-McLeod functions as the inhomogeneous parameter approaches infinity using the Deift-Zhou nonlinear steepest-descent method for Riemann-Hilbert problems. This analysis is done in both the pole-free region and pole region. The asymptotic formulae show excellent agreement with numerically computed solutions in both regions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_08142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large-Parameter Asymptotics of Generalized Hasting-McLeod Functions Schmidt, Kurt Buckingham, Robert Mathematical Physics 33E17 34E05 The generalized Hastings-McLeod solutions to the inhomogeneous Painlevé-II equation arise in multi-critical unitary random matrix ensembles, the chiral two-matrix model for rectangular matrices, non-intersecting squared Bessel paths, and non-intersecting Brownian motions on the circle. We establish the leading-order asymptotic behavior of the generalized Hastings-McLeod functions as the inhomogeneous parameter approaches infinity using the Deift-Zhou nonlinear steepest-descent method for Riemann-Hilbert problems. This analysis is done in both the pole-free region and pole region. The asymptotic formulae show excellent agreement with numerically computed solutions in both regions. |
| title | Large-Parameter Asymptotics of Generalized Hasting-McLeod Functions |
| topic | Mathematical Physics 33E17 34E05 |
| url | https://arxiv.org/abs/2404.08142 |