Random matrices.

By B. Eynard, Taro Kimura, S. Ribault. 2015

584 citations recorded by the source corpus.

We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of algebraic geometry, loop equations and their solution using topological recursion, orthogonal polynomials and their relation with integrable systems. Each approach provides its own definition of the spectral curve, a geometric object which encodes all the properties of a model. We also introduce the two peripheral subjects of counting polygonal surfaces, and computing angular integrals.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/66e65cb7a51cc8c3f09230ce3314710155049058

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In Artificial Intelligence

1. Jordan S. Cotler
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Citations in the corpus

• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral (2020, background): “2 of [52] and for a summary of other interesting properties of the topological recursion [53]).”
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