Biorthogonal measures, polymer partition functions, and random matrices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910677974646784 |
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| author | Cafasso, Mattia Claeys, Tom |
| author_facet | Cafasso, Mattia Claeys, Tom |
| contents | We develop the study of a particular class of biorthogonal measures, encompassing at the same time several random matrix models and partition functions of polymers. This general framework allows us to characterize the partition functions of the Log Gamma polymer and the mixed polymer in terms of explicit biorthogonal measures, as it was previously done for the homogeneous O'Connell-Yor polymer by Imamura and Sasamoto. In addition, we show that the biorthogonal measures associated to these three polymer models (Log Gamma, O'Connell-Yor, and mixed polymer) converge to random matrix eigenvalue distributions in small temperature limits. We also clarify the connection between different Fredholm determinant representations and explain how our results might be useful for asymptotic analysis and large deviation estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Biorthogonal measures, polymer partition functions, and random matrices Cafasso, Mattia Claeys, Tom Mathematical Physics Classical Analysis and ODEs Complex Variables Probability 82D60, 60B20, 60G55 We develop the study of a particular class of biorthogonal measures, encompassing at the same time several random matrix models and partition functions of polymers. This general framework allows us to characterize the partition functions of the Log Gamma polymer and the mixed polymer in terms of explicit biorthogonal measures, as it was previously done for the homogeneous O'Connell-Yor polymer by Imamura and Sasamoto. In addition, we show that the biorthogonal measures associated to these three polymer models (Log Gamma, O'Connell-Yor, and mixed polymer) converge to random matrix eigenvalue distributions in small temperature limits. We also clarify the connection between different Fredholm determinant representations and explain how our results might be useful for asymptotic analysis and large deviation estimates. |
| title | Biorthogonal measures, polymer partition functions, and random matrices |
| topic | Mathematical Physics Classical Analysis and ODEs Complex Variables Probability 82D60, 60B20, 60G55 |
| url | https://arxiv.org/abs/2401.10130 |