Matrix integrals and enumeration of maps

Abstract

This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.

chapter of the "The Oxford Handbook of Random Matrix Theory", editors G. Akemann, J. Baik and P. Di Francesco ; 24 pages and 5 figures

References in corpus (5)

• Geodesic Distance in Planar Graphs
• The degree distribution in bipartite planar maps: applications to the Ising model
• Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model
• Combinatorics of bicubic maps with hard particles
• A bijection for rooted maps on orientable surfaces

Cited by in corpus (3)

• Introduction to Random Matrices - Theory and Practice
• Maps, immersions and permutations
• Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations