Matrix eigenvalue model: Feynman graph technique for all genera

By L. Chekhov, B. Eynard. 2006

163 citations recorded by the source corpus.

We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power β 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).

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6924223ce060b1bdc8018dbc7b6f57748e07dc1d

How researchers see this paper

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In Geometry and Topology

1. Marcos Mariño
2. A. Klemm
3. C. Vafa
4. B. Eynard
5. Mina Aganagic
6. R. Dijkgraaf
7. Min-xin Huang
8. N. Orantin

In Nuclear and High Energy Physics

1. Marcos Mariño
2. A. Klemm
3. C. Vafa
4. Mina Aganagic
5. Min-xin Huang
6. B. Eynard
7. R. Dijkgraaf
8. N. Orantin

In Statistics and Probability

1. B. Eynard
2. A. Klemm
3. N. Orantin
4. Min-xin Huang
5. Gaëtan Borot
6. Alice Guionnet
7. C. Vafa
8. Mina Aganagic

Citations in the corpus

• Holomorphic anomaly in gauge theories and matrix models (2006, methodology): “The B-model iteration in the genus bears some resemblance to the procedure compute higher genus free energy and resolvent of the matrix models for one-cut solution in [12] and generalized to multi-cut solution in [13, 48, 49], where the iteration equation is obtained by doing 1/N expansion in the lo”
• JT gravity and the ensembles of random matrix theory (2019, unknown): “Previous work on the β-ensembles includes [53, 54, 55].”
• Equivalence of ELSV and Bouchard–Mariño conjectures for $$r$$r-spin Hurwitz numbers (2013, background): “In [5, 18] Chekhov, Eynard, and Orantin assigned to every plane analytic complex curve C a series of invariants Wg,n(C) called correlation n-forms.”
• Quantum geometry of refined topological strings (2011, background): “17) and its recursion relation has been studied in [37, 38, 39].”
• The Ω Deformed B-model for Rigid N = 2 Theories (2011, background): “These refined N -matrix ensembles reduce to familiar ensembles in certain limits: ǫ1 = −(1)2ǫ2 corresponds to the standard orthogonal ensemble, and ǫ1 = −2ǫ2 to the symplectic ensemble [29].”
• Asymptotic Expansion of β Matrix Models in the One-cut Regime (2011, methodology): “ut knowledge of W n(for n3). These techniques found their origin in [AM90,ACM92,ACKM93,ACKM95] and culminated with the formalism of the "topological recursion" of [Eyn04,EO07] for = 2, and [CE06] for any xed >0. In this article, we observe that K1 is a continuous operator on some approp”
• Invariants of algebraic curves and topological expansion (2007, background): “are indeed the same. • It would be interesting also to extend our construction to other types of matrix models, for instance non-hermitian (real symmetric or quaternionic). A first attempt was done in [18]. Another possible extension is towards the O(n) matrix model, whose large Nlimit is known in te”