Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains

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
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: 21 Jun 2021 15:33
URI: http://nrl.northumbria.ac.uk/id/eprint/46237

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