Large N expansions and Painlevé hierarchies in the Hermitian matrix model
| dc.contributor.author | Álvarez Galindo, Gabriel | |
| dc.contributor.author | Martínez Alonso, Luis | |
| dc.contributor.author | Medina Reus, Elena | |
| dc.date.accessioned | 2023-06-20T03:31:21Z | |
| dc.date.available | 2023-06-20T03:31:21Z | |
| dc.date.issued | 2011-07-15 | |
| dc.description | © 2011 IOP Publishing Ltd. The financial support of the Universidad Complutense under project GR35/10-A910556, the Comision Interministerial de Ciencia y Tecnología under projects FIS2008-00200 and FIS2008-00209 are gratefully acknowledged. | |
| dc.description.abstract | We present a method to characterize and compute the large N formal asymptotics of regular and critical Hermitian matrix models with general even potentials in the one-cut and two-cut cases. Our analysis is based on a method to solve continuum limits of the discrete string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. This method also leads to an explicit formulation, in terms of coupling constants and critical parameters, of the members of the Painlevé I and Painlevé II hierarchies associated with one-cut and two-cut critical models, respectively. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Universidad Complutense | |
| dc.description.sponsorship | Comisión Interministerial de Ciencia y Tecnología | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20402 | |
| dc.identifier.doi | 10.1007/s11069-011-0048-6 | |
| dc.identifier.issn | 1751-8113 | |
| dc.identifier.officialurl | http://iopscience.iop.org/1751-8121/44/28/285206/pdf/1751-8121_44_28_285206.pdf | |
| dc.identifier.relatedurl | http://iopscience.iop.org | |
| dc.identifier.relatedurl | http://arxiv.org/pdf/1106.0593v1.pdf | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/43700 | |
| dc.issue.number | 28 | |
| dc.journal.title | Journal of Physics A: Mathematical and Theoretical | |
| dc.language.iso | eng | |
| dc.publisher | IOP Publishing Ltd | |
| dc.relation.projectID | GR35/10-A910556 | |
| dc.relation.projectID | FIS2008-00200 | |
| dc.relation.projectID | FIS2008-00209 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Double Scaling Limit | |
| dc.subject.keyword | Partition-Function | |
| dc.subject.keyword | Quantum-Gravity | |
| dc.subject.keyword | Asymptotics | |
| dc.subject.keyword | Universality | |
| dc.subject.keyword | Equations | |
| dc.subject.keyword | Polynomials | |
| dc.subject.keyword | Behavior | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.title | Large N expansions and Painlevé hierarchies in the Hermitian matrix model | |
| dc.type | journal article | |
| dc.volume.number | 44 | |
| dcterms.references | [1] Fokas, A.S., Its, A.R. and Kitaev, A., 1991, Commun. Math. Phys. 2, 313–44. [2] Fokas, A.S., Its, A.R. and Kitaev, A., 1992, Commun. Math. Phys. 2, 395–430. [3] Deift, P., 1999, Orthogonal Polynomials and Random Matrices: A Riemann–Hilbert Approach (Providence, RI: American Mathematical Society). [4] Deift, P., Kriecherbauer, T., McLaughlin, K.T.R., Venakides, S. and Zhou, X., 1999,Commun. Pure Appl. Math.52, 1335–425. [5] Bleher, P., 2008, Lectures on Random Matrix Models: The Riemann–Hilbert Approach (Amsterdam: North-Holland). [6] Martínez Alonso, L. and Medina, E., 2009, J. Phys. A: Math. Theor. 42, 205204. [7] Di Francesco, P., Ginsparg, P. and Zinn-Justin, J., 1995, Phys. Rep. 254, 1–133. [8] Brezin, E., Itzykson, C., Parisi, G. and Zuber, J.B., 1978, Commun. Math. Phys. 59, 35–51. [9] Bessis, D., 1979, Commun. Math. Phys. 69, 147–63. [10] Bessis, D., Itzykson, C. and Zuber, J.B., 1980, Adv. Appl. Math. 1, 109–57. [11] Ercolani, N.M. and McLaughlin, K.D.T.R., 2003, Int. Math. Res. Not. 14, 755–820. [12] Bleher, P.M. and Its, A.R., 2005, Ann. Inst. Fourier (Grenoble) 55, 1943–2000 (available at: http://aif.cedram.org/cedram-bin/article/AIF_2005__55_6_1943_0.pdf). [13] Bonnet, G., David, F. and Eynard, B., 2000, J. Phys. A: Math. Gen. 33, 6739–68. [14] Eynard, B., 2009, J. High Energy Phys. JHEP03(2009)003. [15] Di Francesco, P., Mathieu, P. and Sénéchal, D., 1997, Conformal Field Theory (New York: Springer). [16] Bergére, M. and Eynard, B., 2009, arXiv:0909.0854. [17] Marchal, O. and Caffaso, M., 2010, arXiv:1002.3347. [18] Kudryashov, N.A., 2003, J. Math. Phys. 44, 6160–78. [19] Demeterfi, K., Deo, N., Jain, S. and Tan, C.I., 1990, Phys. Rev. D 42, 4105–22. [20] Bleher, P. and Its, A., 1999, Ann. Math. 150, 185–266. [21] Bleher, P. and Eynard, B., 2003, J. Phys. A: Math. Gen. 36, 3085–105. [22] Bleher, P. and Its, A., 2003, Commun. Pure Appl. Math. 56, 433–516. [23] Martínez Alonso, L. and Medina, E., 2007, J. Phys. A: Math. Theor. 40, 14223–41. [24] Martínez Alonso, L. and Medina, E., 2008, J. Phys. A: Math. Theor. 41, 335202. [25] Álvarez, G., Martínez Alonso, L. and Medina, E., 2010, J. Stat. Mech. P03023. [26] Gerasimov, A., Marshakov, A., Mironov, A., Morozov, A. and Orlov, A., 1991, Nucl. Phys. B 357, 565–618. [27] Kuijlaars, A.B.J., and McLaughlin, K.D., 2000, Commun. Pure Appl. Math. 53, 736–85. [28] Brézin, E., Marinari, E., and Parisi, G., 1990, Phys. Lett. B 242, 35–8. [29] Darboux, G., 1915, Lecons Sur la Theorie General des Surfaces II (Paris: Gauthier-Villars), [30] Eynard, B., 2006, J. Stat. Mech. P07005. [31] Claeys, T., 2008, Int. Math. Res. Not. 2008, rnm166. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 93e2c5ce-9576-43ad-99af-1f18cb650636 | |
| relation.isAuthorOfPublication | 896aafc0-9740-4609-bc38-829f249a0d2b | |
| relation.isAuthorOfPublication.latestForDiscovery | 93e2c5ce-9576-43ad-99af-1f18cb650636 |
