Benassi, Costanza, Dell'Atti, Marta and Moro, Antonio (2021) Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains. Letters in Mathematical Physics, 111 (3). p. 78. ISSN 0377-9017
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Official URL: https://doi.org/10.1007/s11005-021-01416-y
Abstract
The partition function of the Symmetric Matrix Ensemble is identified with the τ−functionof a particular solution of the Pfaff Lattice. We show that, in the case of even power interactions, in the thermodynamic limit, the τ−function corresponds to the solution of anintegrable chain of hydrodynamic type. We prove that the hydrodynamic chain so obtainedis diagonalisable and admits hydrodynamic reductions in Riemann invariants in an arbitrarynumber of components.
| Item Type: | Article |
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| Additional Information: | Funding information: This work is supported by the Leverhulme Trust RPG 2017-228 (PI A.M.). Authors also thank the London Mathematical Society, the Royal Society International Exchanges Grant IES-R2-170116 (PI A.M.), GNFM - Gruppo Nazionale per la Fisica Matematica, INdAM (Istituto Nazionale di Alta Matematica) for supporting activities that contributed to the research reported in this paper. |
| Uncontrolled Keywords: | Random Matrices, Hydrodynamic Integrable Systems, Hydrodynamic Reductions, Gibbons-Tsarev Systems |
| Subjects: | G900 Others in Mathematical and Computing Sciences H800 Chemical, Process and Energy Engineering |
| Department: | Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering |
| Related URLs: | |
| Depositing User: | John Coen |
| Date Deposited: | 20 May 2021 14:58 |
| Last Modified: | 14 Jun 2022 03:30 |
| URI: | http://nrl.northumbria.ac.uk/id/eprint/46237 |
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