Matrix eigenvalue model: Feynman graph technique for all genera

Leonid Chekhov (1, 2, 3) , Bertrand Eynard (4)

1 ISCP - Interdisciplinary Scientific Center Poncelet
2 ITEP - Institute of Theoretical and Experimental Physics [Moscow]
3 SMI | RAS - Steklov Mathematical Institute [Moscow]
4 SPhT - Service de Physique Théorique

We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power $\beta$ by the Vandermonde determinant) to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint intervals (curves).

Mots clés: Random matrices; algebraic geometry; large N; Dyson gas

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Leonid Chekhov, Bertrand Eynard. Matrix eigenvalue model: Feynman graph technique for all genera. 2006. ⟨hal-00022361⟩