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Multiple orthogonal polynomials, string equations and the large-n limit

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dc.contributor.authorMartínez Alonso, Luis
dc.contributor.authorMedina Reus, Elena
dc.date.accessioned2023-06-20T04:00:23Z
dc.date.available2023-06-20T04:00:23Z
dc.date.issued2009-03-22
dc.description©IOP Publishing Ltd. The authors wish to thank the Spanish Ministerio de Educación y Ciencia (research project FIS2008-00200/FIS) for its finantial support. This work is also part of the MISGAM programme of the European Science Foundation.
dc.description.abstractThe Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated with pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the phase space of the Whitham hierarchy of dispersionless integrable systems is provided. Applications to the analysis of the large-n limit of multiple orthogonal polynomials and their associated random matrix ensembles and models of non-intersecting Brownian motions are given.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipSpanish Ministerio de Educación y Ciencia
dc.description.sponsorshipEuropean Science Foundation (MISGAM programme)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/34240
dc.identifier.doi10.1088/1751-8113/42/20/205204
dc.identifier.issn1751-8113
dc.identifier.officialurlhttp://dx.doi.org/10.1088/1751-8113/42/20/205204
dc.identifier.relatedurlhttp://iopscience.iop.org/
dc.identifier.relatedurlhttp://arxiv.org/abs/0812.3817
dc.identifier.urihttps://hdl.handle.net/20.500.14352/44794
dc.issue.number20
dc.journal.titleJournal of physics A: Mathematical and theoretical
dc.language.isoeng
dc.publisherIOP Publishing Ltd
dc.relation.projectIDFIS2008-00200/FIS
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordGaussian random matrices
dc.subject.keywordNonintersecting brownian motions
dc.subject.keywordUniversal whitham hierarchy
dc.subject.keywordExternal source
dc.subject.keywordModels
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleMultiple orthogonal polynomials, string equations and the large-n limit
dc.typejournal article
dc.volume.number42
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 Vol. 3, Amer. Math. Soc., Providence R.I. 1999. [3] A.S. Fokas, A.R. Its and A.V. Kitaev, Commun. Math. Phys. 147, 395 (1992) [4] P. Deift and X. Zhou, Ann. Math. 2, 137 (1993) [5] W. Van Assche, J.S. Geronimo, and A.B.J. Kuijlaars, Riemann-Hilbert problems for multiple orthogonal polynomials, In: Special Functions 2000: Current Perspectives and Future Directions (J. Bustoz et al., eds.), Kluwer, Dordrecht, (2001) 2359. [6] P.M. Bleher and A.B.J. Kuijlaars, Int. Math. Research Notices 2004, no 3 (2004), 109129. [7] P.M. Bleher and A.B.J. Kuijlaars, Comm. Math. Phys. 252 (2004), 4376. [8] A.I. Aptekarev, P.M. Bleher and A.B.J. Kuijlaars, Comm. Math. Phys. 259 (2005), 367289. [9] P.M. Bleher and A.B.J. Kuijlaars, , Comm. Math. Phys. 270 (2007), 481. [10] E. Daems, Asymptotics for non-intersecting Brownian motions using multiple orthogonal polynomials, Ph.D. thesis, K.U.Leuven, 2006, URL http://hdl.handle.net/1979/324. [11] I. M. Krichever, Comm. Pure. Appl. Math. 47 (1994), 437. [12] K. Takasaki and T. Takebe, Rev. Math. Phys. 7, 743 (1995) [13] M. J. Bergvelt and A. P. E. ten Kroode, Pacific J. Math. 171 23 (1995). [14] M. Mañas, E. Medina and L. Mart´ınez Alonso, J. Phys.A: Math. Gen. 39 (2006) 2349. [15] L. Martínez Alonso, E. Medina and M. Mañas, J. Math. Phys. 47 (2006) 083512. [16] K. Takasaki, Dispersionless integrable hierarchies revisited, talk delivered at SISSA at september 2005 (MISGAM program); K. Takasaki and T. Takebe, Physica D 235 (2007) 109. [17] E. Daems and A.B.J. Kuijlaars, J. of Approx. Theory 146 (2007) 91. [18] L. Martínez Alonso and E. Medina, J. Phys.A: Math. Gen. 40 (2007) 14223. [19] L. Martínez Alonso and E. Medina, J. Phys.A: Math. Gen. 41 (2008) 335202. [20] K. Johansson, Probab. Theory Related Fields 123 (2002), 225. [21] M. Katori and H. Tanemura, Phys. Rev. E 66 (2002) Art. No. 011105. [22] T. Nagao and P.J Forrester, Nuclear Phys. B 620 (2002), 551. [23] L. Pastur, Teoret. Mat. Fiz. 10 (1972), 102112. [24] Mark Adler, Pierre van Moerbeke and Pol Vanhaecke, Moment matrices and multi- omponent KP, with applications to random matrix theory, preprint math-ph/0612064
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