Formal multidimensional integrals, stuffed maps, and topological recursion

DOI10.4171/AIHPD/7zbMath1297.05013arXiv1307.4957OpenAlexW2962983978MaRDI QIDQ407409

Gaëtan Borot

Publication date: 1 September 2014

Published in: Annales de l'Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.4957

zbMATH Keywords

matrix modelstopological recursionmap enumerationloop equations2D quantum gravityTutte equation

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Random matrices (algebraic aspects) (15B52) Miscellaneous topics of analysis in the complex plane (30E99)

Related Items

Blobbed topological recursion ⋮ Spectral statistics of Dirac ensembles ⋮ A Givental-like formula and bilinear identities for tensor models ⋮ A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions ⋮ Blobbed topological recursion of the quartic Kontsevich model. I: Loop equations and conjectures ⋮ Double scaling limits of Dirac ensembles and Liouville quantum gravity ⋮ Complete solution of the LSZ model via topological recursion ⋮ Generalised ordinary vs fully simple duality for \(n\)-point functions and a proof of the Borot-Garcia-Failde conjecture ⋮ Blobbed topological recursion: properties and applications ⋮ Nesting statistics in the \(O(n)\) loop model on random planar maps ⋮ Simple maps, Hurwitz numbers, and topological recursion ⋮ Colored triangulations of arbitrary dimensions are stuffed Walsh maps ⋮ Relating ordinary and fully simple maps via monotone Hurwitz numbers ⋮ From scalar fields on quantum spaces to blobbed topological recursion ⋮ From noncommutative geometry to random matrix theory

Cites Work

• Geometry of spectral curves and all order dispersive integrable system
• The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
• The Laplace transform of the cut-and-join equation and the Bouchard-Mariño conjecture on Hurwitz numbers
• A matrix model for simple Hurwitz numbers, and topological recursion
• Hermitian matrix model free energy: Feynman graph technique for all genera
• Free energy topological expansion for the 2-matrix model
• Remodeling the B-model
• Invariants of algebraic curves and topological expansion
• Torus knots and mirror symmetry
• Planar diagrams
• Exact solution of the \(O(n)\) model on a random lattice
• Asymptotic expansion of \(\beta \) matrix models in the one-cut regime
• Matrix model calculations beyond the spherical limit.
• All order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials
• Computation of open Gromov-Witten invariants for toric Calabi-Yau 3-folds by topological recursion, a proof of the BKMP conjecture
• Abstract loop equations, topological recursion and new applications
• More on theO(n) model on random maps via nested loops: loops with bending energy
• Large-NAsymptotic Expansion for Mean Field Models with Coulomb Gas Interaction
• Breakdown of universality in multi-cut matrix models
• Topological expansion of mixed correlations in the Hermitian 2-matrix model andx–ysymmetry of theF_galgebraic invariants
• On the \(1/n\) expansion for some unitary invariant ensembles of random matrices