Matrix models and random surfaces
by Alex Lee
Abstract: Statistical mechanical partition functions involving matrices, otherwise known as matrix models, can be interpreted as generating functions of random surfaces, that is, discrete surfaces built by gluing together polygons in various configurations. In this context, expectation values of traces are generating functions of random surfaces
with boundaries and these functions then obey what are known as loop equations for the matrix model. Finally, I will mention applications of
matrix models to counting quadrangulations of surfaces.
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