Bordered and Framed Toeplitz and Hankel Determinants with Applications to Integrable Probability
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910475349917696 |
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| author | Gharakhloo, Roozbeh Liechty, Karl |
| author_facet | Gharakhloo, Roozbeh Liechty, Karl |
| contents | Bordered and framed Toeplitz/Hankel determinants have the same structure as Toeplitz/Hankel determinants except in small number of matrix rows and/or columns. We review these structured determinants and their connections to orthogonal polynomials, collecting well-known and perhaps less well-known results. We present some applications for these structured determinants to ensembles of non-intersecting paths and the six-vertex model, with an eye towards asymptotic analysis. We also prove some asymptotic formulae for the probability of non-intersection for an ensemble of continuous time random walks for certain choices of starting and ending points as the number of random walkers tends to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bordered and Framed Toeplitz and Hankel Determinants with Applications to Integrable Probability Gharakhloo, Roozbeh Liechty, Karl Classical Analysis and ODEs Mathematical Physics Probability Bordered and framed Toeplitz/Hankel determinants have the same structure as Toeplitz/Hankel determinants except in small number of matrix rows and/or columns. We review these structured determinants and their connections to orthogonal polynomials, collecting well-known and perhaps less well-known results. We present some applications for these structured determinants to ensembles of non-intersecting paths and the six-vertex model, with an eye towards asymptotic analysis. We also prove some asymptotic formulae for the probability of non-intersection for an ensemble of continuous time random walks for certain choices of starting and ending points as the number of random walkers tends to infinity. |
| title | Bordered and Framed Toeplitz and Hankel Determinants with Applications to Integrable Probability |
| topic | Classical Analysis and ODEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2401.01971 |