Fetching the paper…
Reading the bibliography…
Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory,...
G.H. Hardy, Sur les zéros de la fonction ζ ( s ) \zeta(s) de Riemann , C.R. Acad. Sci. Paris 158
1914
Earlier work this paper cites.
J. Wishart, The generalised product moment distribution in samples from a normal multivariate population , Biometrika 20A
1928
Earlier work this paper cites.
A. Selberg, Bemerkninger om et multiplet integral , Norsk. Mat. Tid. 26
1944
Earlier work this paper cites.
1945
Earlier work this paper cites.
E.P. Wigner, On the statistical distribution of the widths and spacings of nuclear resonance levels , Proc. Cambridge Phil. Soc. 47
1951
Earlier work this paper cites.
G. Szegö, On certain hermitian forms associated with the Fourier series of a positive function , Comm. Sém. Math. Univ. Lund (1952), 228–238, tome supplémentaire
1952
Earlier work this paper cites.
Harish-Chandra, Differential operators on a semi-simple Lie algebra , J. Amer. Math. 79
1957
Earlier work this paper cites.
C. Berge, Théorie des graphes et ses applications , Dunod, Paris, 1958
1958
Earlier work this paper cites.
S. Karlin and J. McGregor, Coincidence probabilities , Pacific J. Math. 9
1959
Earlier work this paper cites.
H.E. Rauch, Weierstrass points, branch points, and moduli of Riemann surfaces , Comm. Pure Appl. Math. 12
1959
Earlier work this paper cites.
M.L. Mehta, On the statistical properties of the level-spacings in nuclear spectra , Nucl. Phys. 18
1960
Earlier work this paper cites.
M.L Mehta and M. Gaudin, On the density of eigenvalues of a random matrix , Nucl. Phys. 18
1960
Earlier work this paper cites.
C.E. Porter and N. Rosenzweig, "Repulsion of energy levels" in complex atomic spectra , Phys. Rev. 120
1960
Earlier work this paper cites.
N.I. Akhiezer, Continuous analogues of the polynomials orthogonal on the system of intervals , Dokl. Akad. Nauk SSSR 141
1961
Earlier work this paper cites.
F. Dyson, Statistical theory of the energy levels of complex systems , J. Math. Phys. 3
1962
Earlier work this paper cites.
W.T. Tutte, A census of planar triangulations , Can. J. Math. 14
1962
Earlier work this paper cites.
H.F. Bückner, On a class of singular integral equation , J. Math. Anal. App. 14
1966
Earlier work this paper cites.
J. Fay, Theta functions on Riemann surfaces , Lecture Notes in Mathematics, vol. 352, Springer, Berlin, 1970
1970
Earlier work this paper cites.
B. Kadomtsev and V. Petviashvili, On the stability of solitary waves in weakly dispersive media , Soviet Phys. Dokl. 15
1970
Earlier work this paper cites.
H.L. Montgomery, The pair correlation of zeroes of the zeta function , Analytic number theory (Amer. Math. Soc., ed.), Proc. Sympos. Pure Math., 1973, http ://www-personal.umich.edu/
1973
Earlier work this paper cites.
M. Ablowitz, D. Kaup, A.C. Newell, and H. Segur, The inverse scattering transform-fourier analysis for nonlinear problems , Stud. Appl. Math. 53
1974
Earlier work this paper cites.
G. t’Hooft, A planar diagram theory for strong interactions , Nucl. Phys. B 72
1974
Earlier work this paper cites.
I. Krichever, Methods of algebraic geometry in the theory of non linear equations , Russ. Math. Surv. 32
1977
Earlier work this paper cites.
É. Brézin, C. Itzykson, G. Parisi, and J.-B. Zuber, Planar diagrams , Commun. Math. Phys. 59
1978
Earlier work this paper cites.
S.W. McDonald and A.N. Kaufman, Spectrum and eigenfunctions for a hamiltonian with stochastic trajectories , Phys. Rev. Lett. 42
1979
Earlier work this paper cites.
H. Flaschka and A.C. Newell, Monodromy- and spectrum-preserving deformations, I , Commun. Math. Phys. 76
1980
Earlier work this paper cites.
S.P. Hastings and J.B. McLeod, A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation , Archive for Rational Mechanics and Analysis 73
1980
Earlier work this paper cites.
C. Itzykson and J.-B. Zuber, The planar approximation II , J. Math. Phys. 21
1980
Earlier work this paper cites.
M. Jimbo, T. Miwa, and K. Ueno, Monodromy preserving deformation of linear ordinary differential equations with rational coefficients : I. General theory and τ \tau -function , Physica D 2
1981
Earlier work this paper cites.
R.B. Laughlin, Anomalous quantum hall effect : an incompressible quantum fluid with fractionally charged excitations , Phys. Rev. Lett. 50
1983
Earlier work this paper cites.
B. Malgrange, Sur les déformations isomonodromiques. i. singularités régulières , Progr. Math., vol. 37, pp. 401–426, Birkhäuser, Boston, 1983
1983
Earlier work this paper cites.
D. Mumford, Towards an enumerative geometry of the moduli space of curves , pp. 271–328, Birkhäuser, 1983
1983
Earlier work this paper cites.
M. Sato and Y. Sato, Soliton equations as dynamical systems on infinite-dimensional grassmann manifold , Nonlinear partial differential equations in applied science, Stud. Math., vol. 81, Tokyo, North Holland, 1983, http ://www.kurims.kyoto-u.ac.jp/ kyodo/kokyuroku/contents/pdf/0439-5.pdf , pp. 259–271
1983
Earlier work this paper cites.
O. Bohigas, M.J. Giannoni, and C. Schmit, Characterization of chaotic quantum spectra and universality of level fluctuation laws , Phys. Rev. Lett. 52
1984
Earlier work this paper cites.
K. Strebel, Quadratic differentials , vol. 3, Ergebnisse der Mathematik und ihrer Grenzgebiete, no. 5, Springer-Verlag, Berlin, 1984
1984
Earlier work this paper cites.
F.G. Tricomi, Integral equations , Interscience, London, 1957, New edition, Dover Publications, 1985
1985
Earlier work this paper cites.
J. Harer and D. Zagier, The Euler characteristics of the moduli space of curves , Invent. Math. 85
1986
Earlier work this paper cites.
V. Kazakov, Ising model on a dynamical planar random lattice : exact solution , Phys. Lett. A 119
1986
Earlier work this paper cites.
A. Odlyzko, On the distribution of spacings between zeros of the zeta function , Math. Comp. 48
1987
Earlier work this paper cites.
A. Voros, Spectral functions, special functions, and the Selberg zeta function , Commun. Math. Phys. 110
1987
Earlier work this paper cites.
B. Duplantier and I.K. Kostov, Conformal spectra of polymers on a random surface , Phys. Lett. Rev. 61
1988
Earlier work this paper cites.
V.G. Knizhnik, A.M. Polyakov, and A.B. Zamolodchikov, Fractal structure of 2 d 2d quantum gravity , Mod. Phys. Lett. A 3
1988
Earlier work this paper cites.
D.R. Guo and Z.X. Wang, Special functions , World Scientific, Singapore, 1989
1989
Earlier work this paper cites.
I.K. Kostov, 𝒪 ( 𝔫 ) \mathcal{O}(\mathfrak{n}) vector model on a planar random lattice : spectrum of anomalous dimensions , Mod. Phys. Lett. A 4
1989
Earlier work this paper cites.
J. Ambjørn and Yu. Makeenko, Properties of loop equations for the hermitian matrix model and for two-dimensional gravity , Mod. Phys. Lett. A 5
1990
Earlier work this paper cites.
E.A. Bender and R. Canfield, The number of rooted maps on an orientable surface , J. Comb. Theo. B 53
1990
Cited alongside, same era.
D. Gross and A. Migdal, A nonperturbative treatment of two-dimensional gravity , Nucl. Phys. B 340
1990
Cited alongside, same era.
J. de Boer, Multi-matrix models and the KP hierarchy , Nucl. Phys B 366
1991
Cited alongside, same era.
J. Ambjørn, L.O. Chekhov, and Yu. Makeenko, Higher genus correlators from the hermitian one-matrix model , Phys. Lett. B 282
1992
Cited alongside, same era.
B. Eynard and J. Zinn-Justin, The 𝒪 ( 𝔫 ) \mathcal{O}(\mathfrak{n}) model on a random surface : critical points and large order behavior , Nucl. Phys. B 386
1992
Cited alongside, same era.
A.Iu. Bejan, Largest eigenvalues and sample covariance matrices. Tracy-Widom and Painlevé II : computational aspects and realization in S-plus with applications , 2005, http ://www.cl.cam.ac.uk/
2005
Later among the works it cites.
B. Eynard and N. Orantin, Mixed correlation functions in the 2 2 -matrix model, and the Bethe ansatz , JHEP (2005), no. 0508 :028, hep-th/0504029
2005
Later among the works it cites.
M. Mariño, Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants , Commun. Math. Phys. 253
2005
Later among the works it cites.
L.O. Chekhov and B. Eynard, Matrix eigenvalue model : Feynman graph technique for all genera , JHEP (2006), no. 0612 :026, math-ph/0604014
2006
Later among the works it cites.
L.O. Chekhov, B. Eynard, and N. Orantin, Free energy topological expansion for the 2-matrix model , JHEP (2006), no. 0612 :053, math-ph/0603003
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A.S. Fokas, A. Its, and A. Kitaev, The isomonodromy approach to matrix models in 2 d 2d quantum gravity , Commun. Math. Phys. 147
1992
Cited alongside, same era.
M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function , Commun. Math. Phys. 147
1992
Cited alongside, same era.
I.K. Kostov and M. Staudacher, Multicritical phases of the 𝒪 ( 𝔫 ) \mathcal{O}(\mathfrak{n}) model on a random lattice , Nucl. Phys. B 384
1992
Cited alongside, same era.
P. Bouwknegt and K. Schoutens, 𝒲 \mathcal{W} -symmetry in conformal field theory , Phys.Rept. 223
1993
Cited alongside, same era.
M. Bershadsky, S. Cecotti, H. Ooguri, and C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes , Commun. Math. Phys. 165
1994
Cited alongside, same era.
P. di Francesco, P. Ginsparg, and J. Zinn-Justin, 2 d 2d gravity and random matrices , Phys. Rep. 254
1994
Cited alongside, same era.
I. Krichever, The Tau function of the universal Whitham hierarchy, matrix models and topological field theories , Comm. Pure Appl. Math. 47
1994
Cited alongside, same era.
2006
Later among the works it cites.
D.S. Dean and S.N. Majumdar, Large deviations of extreme eigenvalues of random matrices , Phys. Rev. Lett. 97
2006
Later among the works it cites.
A. Fokas, A. Its, A. Kapaev, and V. Novokshenov, Painlevé transcendents : the Riemann-hilbert approach , Mathematical Surveys and Monographs, vol. 128, American Mathematical Society, 2006
2006
Later among the works it cites.
M.C.-C. Liu, Formulae of one-partition and two-partition Hodge integrals , Geom. Topol. Monogr. 8 (2006), 105–128
2006
Later among the works it cites.
S. Smirnov, Towards conformal invariance of 2 d 2d lattice models , Proc. Int. Congr. Math. 2
2006
Later among the works it cites.
P. Wiegmann and A. Zabrodin, Large N N expansion for the 2 D 2D Dyson gas , J. Phys. A 39
2006
Later among the works it cites.
G. Akemann, Matrix models and QCD with chemical potential , Int. J. Mod. Phys. A 22
2007
Later among the works it cites.
2007
Later among the works it cites.
P. Deift and D. Gioev, Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices , Comm. Pure Appl. Math. 60
2007
Later among the works it cites.
B. Eynard, M. Mariño, and N. Orantin, Holomorphic anomaly and matrix models , JHEP (2007), no. 0706 :058, hep-th/0702110
2007
Later among the works it cites.
H. Farkas and I. Kra, Riemann surfaces , second ed., Graduate Texts in Mathematics, Springer, Berlin, 2007
2007
Later among the works it cites.
M. Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces , Invent. math. 167
2007
Later among the works it cites.
N. Orantin, Du développement topologique des modèles de matrices à la théorie des cordes topologiques : combinatoire de surfaces par la géométrie algébrique , Thèse de doctorat, Université Paris VI (2007), http ://tel.archives-ouvertes.fr/tel-00173162/en/
2007
Later among the works it cites.
2008
Later among the works it cites.
P. Deift, A. Its, and I. Krasovsky, Asymptotics of the Airy-kernel determinant , Commun. Math. Phys. 278
2008
Later among the works it cites.
P.J. Forrester and S.O. Warnaar, The importance of the Selberg integral , Bull. Amer. Math. Soc. 45
2008
Later among the works it cites.
J.L. Jacobsen and H. Saleur, Conformal boundary loop models , Nucl. Phys. B 88
2008
Later among the works it cites.
V.B. Matveev, 30 30 years of finite-gap integration theory , Phil. Trans. R. Soc. A 366
2008
Later among the works it cites.
M. Mulase and B. Safnuk, A simple proof of Mirzakhani’s recursion formula of Weil-Petersson volumes , Ind. J. Math. 50
2008
Later among the works it cites.
V. Bouchard, A. Klemm, M. Mariño, and S. Pasquetti, Remodeling the B-model , Commun. Math. Phys. 287
2009
Later among the works it cites.
2009
Later among the works it cites.
M. Bertola and M.Y. Mo, Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights , Adv. Math. 220
2009
Later among the works it cites.
G. Chapuy, Combinatoire bijective des cartes de genre supérieur , Thèse de doctorat, École Polytechnique (2009), http ://tel.archives-ouvertes.fr/pastel-00005289/
2009
Later among the works it cites.
S. Caracciolo and A. Sportiello, Spanning forests on random planar lattices , J. Stat. Phys. 135
2009
Later among the works it cites.
2009
Later among the works it cites.
P. Flajolet and R. Sedgewick, Analytic combinatorics , Cambridge University Press, 2009, http ://algo.inria.fr/flajolet/Publications/books.html
2009
Later among the works it cites.
J. Li, M.C.-C. Liu, K. Liu, and J. Zhou, A mathematical theory of the topological vertex , Geom. Topol. 13
2009
Later among the works it cites.
2009
Later among the works it cites.
2009
Later among the works it cites.
2009
Later among the works it cites.
2010
Later among the works it cites.
2010
Later among the works it cites.
J.-E. Bourgine, Modèles de matrices et problèmes de bord dans la gravité de Liouville , Thèse de doctorat, Université d’Orsay-Paris Sud (2010), http ://hal.archives-ouvertes.fr/tel-00541162/
2010
Later among the works it cites.
J. Dubail, Conditions aux bords dans des théories conformes non unitaires , Thèse de doctorat, Université d’Orsay-Paris Sud (2010), http ://tel.archives-ouvertes.fr/docs/00/55/56/24/PDF/pres.pdf
2010
Later among the works it cites.
P.J. Forrester, Log-gases and random matrices , Princeton University Press, 2010
2010
Later among the works it cites.
B. Rider, Exposé au MSRI Semester on Random Matrix Theory
2010
Later among the works it cites.
2010
Later among the works it cites.
2010
Later among the works it cites.
I.K. Kostov and N. Orantin, CFT and topological recursion , math-ph/1006.2028
2028
Closest in time.