Geodesic
Logarithmic potential $\beta$-ensembles and Feynman graphs
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Tome 272 (2011), pp. 65-83.

Voir la notice de l'article provenant de la source Math-Net.Ru

We present a diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with an arbitrary power of the Vandermonde determinant) to all orders of the $1/N$ expansion in the case when the limiting eigenvalue distribution spans an arbitrary (but fixed) number of disjoint intervals (curves) and when logarithmic terms are present. This diagrammatic technique is corrected and refined as compared to our first paper with B. Eynard of 2006. 
@article{TM_2011_272_a6,
     author = {L. O. Chekhov},
     title = {Logarithmic potential $\beta$-ensembles and {Feynman} graphs},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {65--83},
     publisher = {mathdoc},
     volume = {272},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_272_a6/}
}
TY  - JOUR
AU  - L. O. Chekhov
TI  - Logarithmic potential $\beta$-ensembles and Feynman graphs
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2011
SP  - 65
EP  - 83
VL  - 272
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2011_272_a6/
LA  - ru
ID  - TM_2011_272_a6
ER  - 
%0 Journal Article
%A L. O. Chekhov
%T Logarithmic potential $\beta$-ensembles and Feynman graphs
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2011
%P 65-83
%V 272
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2011_272_a6/
%G ru
%F TM_2011_272_a6
L. O. Chekhov. Logarithmic potential $\beta$-ensembles and Feynman graphs. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of modern theoretical and mathematical physics: Gauge theories and superstrings, Tome 272 (2011), pp. 65-83. http://geodesic.mathdoc.fr/item/TM_2011_272_a6/

[1] Alday L.F., Gaiotto D., Tachikawa Y., “Liouville correlation functions from four-dimensional gauge theories”, Lett. Math. Phys., 91 (2010), 167–197, arXiv: 0906.3219 [hep-th] | DOI | MR | Zbl

[2] Borot G., Eynard B., Majumdar S.N., Nadal C., Large deviations of the maximal eigenvalue of random matrices, E-print, 2010, arXiv: 1009.1945 [math-ph] | MR

[3] Chekhov L.O., “Popravki roda odin k mnogorazreznym resheniyam matrichnoi modeli”, TMF, 141:3 (2004), 358–374, arXiv: hep-th/0401089 | DOI | MR

[4] Chekhov L., Eynard B., “Hermitian matrix model free energy: Feynman graph technique for all genera”, J. High Energy Phys., 2006, no. 3, Pap. 014 | MR

[5] Chekhov L., Eynard B., “Matrix eigenvalue model: Feynman graph technique for all genera”, J. High Energy Phys., 2006, no. 12, Pap. 026 | MR

[6] Dijkgraaf R., Vafa C., Toda theories, matrix models, topological strings, and $N=2$ gauge systems, E-print, 2009, arXiv: 0909.2453 [hep-th]

[7] Eguchi T., Maruyoshi K., “Penner type matrix model and Seiberg–Witten theory”, J. High Energy Phys., 2010, no. 2, Pap. 022, arXiv: 0911.4797 [hep-th] | MR

[8] Eynard B., “Topological expansion for the 1-Hermitian matrix model correlation functions”, J. High Energy Phys., 2004, no. 11, Pap. 031, arXiv: hep-th/0407261 | MR

[9] Mironov A., Morozov A., “The power of Nekrasov functions”, Phys. Lett. B, 680 (2009), 188–194, arXiv: 0908.2190 [hep-th] | DOI | MR

[10] Marshakov A., Mironov A., Morozov A., “On non-conformal limit of the AGT relations”, Phys. Lett. B, 682 (2009), 125–129, arXiv: 0909.2052 [hep-th] | DOI | MR

[11] Marshakov A., Mironov A., Morozov A., “Zamolodchikov asymptotic formula and instanton expansion in $\mathcal N=2$ SUSY $N_f=2N_c$ QCD”, J. High Energy Phys., 2009, no. 11, Pap. 048, arXiv: 0909.3338 [hep-th] | MR