On the singular sector of the Hermitian random matrix model in the large N limit
| dc.contributor.author | Konopelchenko, Boris | |
| dc.contributor.author | Martínez Alonso, Luis | |
| dc.contributor.author | Medina Reus, Elena | |
| dc.date.accessioned | 2023-06-20T04:00:18Z | |
| dc.date.available | 2023-06-20T04:00:18Z | |
| dc.date.issued | 2011-01-31 | |
| dc.description | ©2010 Elsevier B.V. All rights reserved. The authors wish to thank the Spanish Ministerio de Educación y Ciencia (research project FIS2008-00200/FIS) for its finantial support. B. K. is thankful to the Departamento de Física Teórica II for the kind hospitality | |
| dc.description.abstract | The one-cut case of the Hermitian random matrix model in the large N limit is considered. Its singular sector in the space of coupling constants is analyzed from the point of view of the hodograph equations of the underlying dispersionless Toda hierarchy. A deep connection with the singular sector of the hodograph equations of the 1-layer Benney (classical long wave equation) hierarchy is stablished. This property is a consequence of the fact that the hodograph equations for both hierarchies describe the critical points of solutions of Euler- Poisson-Darboux equations. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spanish Ministerio de Educación y Ciencia | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/34203 | |
| dc.identifier.doi | 10.1016/j.physleta.2010.12.055 | |
| dc.identifier.issn | 0375-9601 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1016/j.physleta.2010.12.055 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.relatedurl | http://arxiv.org/abs/1005.4773 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/44792 | |
| dc.issue.number | 5 | |
| dc.journal.title | Physics letters A | |
| dc.language.iso | eng | |
| dc.page.final | 872 | |
| dc.page.initial | 867 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | FIS2008-00200/FIS | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Integrable systems | |
| dc.subject.keyword | Hodograph equations | |
| dc.subject.keyword | Random matrix models | |
| dc.subject.keyword | Euler-Poisson-Darboux equation | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | On the singular sector of the Hermitian random matrix model in the large N limit | |
| dc.type | journal article | |
| dc.volume.number | 375 | |
| dcterms.references | [1] P. Di Francesco, P. Ginsparg and Z. Zinn-Justin, Phys. Rept. 254,1 (1995) [2] P. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics 3, Amer. Math. Soc. Providence, RI, (1999) [3] L. Martínez Alonso and E. Medina, J. Phys. A: Math. Gen. 40, 14223 (2007) [4] L. Martínez Alonso and E. Medina, J. Phys. A: Math. Gen. 41, 335202 (2008) [5] B. A. Dubrovin and S. P. Novikov, Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory, Russian Math. Surveys 44, 35 (1989) [6] C. P. Boyer and J. D. Finley, J. Math. Phys., 23, 1126 (1982) [7] M. Mineev- Weinstein, P. Wiegman and A. Zabrodin, Phys. Rev. Lett., 84, 5106 (2000) [8] P. W. Wiegman and P. B. Zabrodin, Comm. Math. Phys., 213, 523 (2000) [9] I. Krichever, M.Mineev- Weinstein, P. Wiegman and A. Zabrodin, Physica D, 198, 1 (2004) [10] D. Y. Benney, Stud. Appl. Math. 52 45-50 (1973). [11] V. E. Zakharov, Func. Anal. Appl. 14, 89 (1980). [12] B. Dubrovin, T. Grava and C. Klein, J. Nonlinear Science 19 57 (2009). [13] B.G. Konopelchenko, L. Martínez Alonso and E. Medina. Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation. arXiv:1003.2892. To appear in J. Phys. A. [14] Y. Kodama and B.G. Konopelchenko, J. Phys. A: Math. Gen. 35, L489-L500 (2002). [15] G. Darboux, Lecons sur la theorie general des surfaces II , Gauthier Villars (1915). [16] V. R. Kudashev and S. E. Sharapov, Phys. Lett. A 154,445 (1991); Theor. Math. Phys. 87, 40 (1991). [17] F. R. Tian, Duke Math. J. 74 203 (1994). [18] M. V. Pavlov, Hamiltonian formulation of electroforesis equations. Integrable hydrodynamic equations Preprint, Landau Inst. Theor. Phys., Chernogolovsca (1987). [19] B.G. Konopelchenko and L. Mart´ınez Alonso, J. Phys. A: Math. Gen. 37, 7859 (2004) [20] I. M. Krichever, Commun. Pure. Appl. Math. 47 437 (1994) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 896aafc0-9740-4609-bc38-829f249a0d2b | |
| relation.isAuthorOfPublication.latestForDiscovery | 896aafc0-9740-4609-bc38-829f249a0d2b |
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