2D QUANTUM GRAVITY,MATRIX MODELS AND GRAPH COMBINATORICS

@inproceedings{Francesco20042DQG,
  title={2D QUANTUM GRAVITY,MATRIX MODELS AND GRAPH COMBINATORICS},
  author={Philippe Di Francesco},
  year={2004}
}
Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004. 
MATRIX MODELS AND TOPOLOGICAL STRINGS
These are lecture notes for my course of the ENRAGE School, april 15–19, 2007, Barcelona (Catalonia).
From operads and PROPs to Feynman Processes
Operads and PROPs are presented, together with examples and applications to quantum physics suggesting the structure of Feynman categories/PROPs and the corresponding algebras.
Generation of matrix models by Ŵ-operators
We show that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of operators. A number of illustrations is given, including the Gaussian
Asymptotic Behavior of Partition Functions with Graph Laplacian
We introduce the matrix sums that represent a discrete analog of the matrix models with quartic potential. The probability space is given by the set of all simple n-vertex graphs with the Gibbs
Exact Results in Five-Dimensional Gauge Theories : On Supersymmetry, Localization and Matrix Models
Gauge theories are one of the corner stones of modern theoretical physics. They describe the nature of all fundamental interactions and have been applied in multiple branches of physics. The most c
Another derivation of the geometrical KPZ relations
We give a physicist's derivation of the geometrical (in the spirit of Duplantier–Sheffield) KPZ relations, via heat kernel methods. It gives a covariant way to define neighborhoods of fractals in 2D
Matrix Resolvent and the Discrete KdV Hierarchy
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution
Generating series for GUE correlators
TLDR
An efficient recursive procedure for computing the correlators in full genera is developed on the Toda lattice hierarchy to computation of logarithmic derivatives of tau-functions in terms of the so-called matrix resolvents of the corresponding difference Lax operator.
On the phase structure of commuting matrix models
A bstractWe perform a systematic study of commutative SO(p) invariant matrix models with quadratic and quartic potentials in the large N limit. We find that the physics of these systems depends
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