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arXiv · 1204.3953

Faces of matrix models

A. Morozov
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Abstract

Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry prepotentials, as result of the action of W-operators and of various recursions on elementary input data, as gluing of certain elementary building blocks. All this explains the central role of such matrix models in modern mathematical physics: they provide the basic "special functions" to express the answers and relations between them, and they serve as a dream model of what one should try to achieve in any other field.

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A. Morozov. 2012-04-18. Faces of matrix models. https://doi.org/10.1134/s0021364012110069

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