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References

  1. Bessis, D.; Itzykson, C.; Zuber, J. B. Quantum field theory techniques in graphical enumeration. Adv. in Appl. Math. 1 (1980), no. 2, 109--157. MR0603127 (83j:81067)
  2. Bryc, Wƚodzimierz. Compound real Wishart and $q$-Wishart matrices. Int. Math. Res. Not. IMRN 2008, Art. ID rnn 079, 42 pp. MR2439565
  3. Dumitriu, Ioana; Edelman, Alan. Global spectrum fluctuations for the $\beta$-Hermite and $\beta$-Laguerre ensembles via matrix models. J. Math. Phys. 47 (2006), no. 6, 063302, 36 pp. MR2239975 (2007e:82014)
  4. Ercolani, N. M.; McLaughlin, K. D. T.-R. Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques and applications to graphical enumeration. Int. Math. Res. Not. 2003, no. 14, 755--820. MR1953782 (2005f:82048)
  5. Goulden, I. P.; Harer, J. L.; Jackson, D. M. A geometric parametrization for the virtual Euler characteristics of the moduli spaces of real and complex algebraic curves. Trans. Amer. Math. Soc. 353 (2001), no. 11, 4405--4427 (electronic). MR1851176 (2002g:14035)
  6. Goulden, I. P.; Jackson, D. M. Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions. Trans. Amer. Math. Soc. 348 (1996), no. 3, 873--892. MR1325917 (96m:05196)
  7. Goulden, I. P.; Jackson, D. M. Maps in locally orientable surfaces, the double coset algebra, and zonal polynomials. Canad. J. Math. 48 (1996), no. 3, 569--584. MR1402328 (97h:05051)
  8. Goulden, I. P.; Jackson, D. M. Maps in locally orientable surfaces and integrals over real symmetric surfaces. Canad. J. Math. 49 (1997), no. 5, 865--882. MR1604106 (99d:05042)
  9. Guionnet, Alice; Maurel-Segala, Edouard. Combinatorial aspects of matrix models. ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006), 241--279 (electronic). MR2249657 (2007g:05087)
  10. Hanlon, Philip J.; Stanley, Richard P.; Stembridge, John R. Some combinatorial aspects of the spectra of normally distributed random matrices. Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991), 151--174, Contemp. Math., 138, Amer. Math. Soc., Providence, RI, 1992. MR1199126 (93j:05164)
  11. Harer, J., and Zagier, D. The Euler characteristic of the moduli space of curves. Inventiones Mathematicae 85, 3 (1986), 457--485.
  12. Isserlis, L. On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables. Biometrika 12, 1/2 (1918), 134--139.
  13. Jackson, D. M. On an integral representation for the genus series for $2$-cell embeddings. Trans. Amer. Math. Soc. 344 (1994), no. 2, 755--772. MR1236224 (94k:05071)
  14. Janson, Svante. Gaussian Hilbert spaces.Cambridge Tracts in Mathematics, 129. Cambridge University Press, Cambridge, 1997. x+340 pp. ISBN: 0-521-56128-0 MR1474726 (99f:60082)
  15. Jüngling, K.; Oppermann, R. Effects of spin interactions in disordered electronic systems: loop expansions and exact relations among local gauge invariant models. Z. Phys. B 38 (1980), no. 2, 93--109. MR0575502 (81d:82038)
  16. Kodama, Y., and Pierce, V.U. Combinatorics of dispersionless integrable systems and universality in random matrix theory, 2008. arxiv:0811.0351.
  17. Ledoux, M. A recursion formula for the moments of the Gaussian Orthogonal Ensemble. Ann. Inst. H. PoincarÈ Probab. Statist. (2007). (to appear).
  18. Leonov, V. P.; Sirjaev, A. N. On a method of semi-invariants. Theor. Probability Appl. 4 1959 319--329. MR0123345 (23 #A673)
  19. Maurel-Segala, E. High order expansion of matrix models and enumeration of maps, 2006. arXiv:math.PR/0608192.
  20. Mkrtchyan, R. The equivalence of $sp(2n)$ and $so(-2n)$ gauge theories. Phys. Letters B105 (1981), 174--176.
  21. Mulase, Motohico; Waldron, Andrew. Duality of orthogonal and symplectic matrix integrals and quaternionic Feynman graphs. Comm. Math. Phys. 240 (2003), no. 3, 553--586. MR2005857 (2004j:81114)
  22. Speed, T. P. Cumulants and partition lattices. Austral. J. Statist. 25 (1983), no. 2, 378--388. MR0725217 (85f:62020)
  23. t'Hooft, G. A planar diagram theory for strong interactions. Nuclear Physics B 72 (1974), 461--473.
  24. Vakhaniya, N. N. Random vectors with values in quaternion Hilbert spaces.(Russian) Teor. Veroyatnost. i Primenen. 43 (1998), no. 1, 18--40; translation in Theory Probab. Appl. 43 (1999), no. 1, 99--115 MR1669968 (2000b:60014)
  25. Wegner, F. Algebraic derivation of symmetry relations for disordered electronic systems. Z. Phys. B 49, 4 (1982), 297--302.
  26. Wick, G. C. The evaluation of the collision matrix. Physical Rev. (2) 80, (1950). 268--272. MR0038281 (12,380d)
  27. Witten, Edward. Baryons and branes in anti-de Sitter space. J. High Energy Phys. 1998, no. 7, Paper 6, 39 pp. (electronic). MR1645043 (99f:81180)


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