Introduction to Monte Carlo for Matrix Models
arXiv:2111.02410 · doi:10.21468/SciPostPhysLectNotes.46
Abstract
We consider a wide range of matrix models and study them using the Monte Carlo technique in the large limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two matrices. We then present new results for several unsolved multi-matrix models where no other tool is yet available. In order to encourage an exchange of ideas between different numerical approaches to matrix models, we provide programs in Python that can be easily modified to study potentials other than the ones discussed. These programs were tested on a laptop and took between a few minutes to several hours to finish depending on the model, , and the required precision.
arXiv commentv2: Added some more text and references, 55 pages, 63 references, 15 figures. All else same as v1. To be published in SciPost Physics Lecture Notes. v1: 52 pages with a few Mathematica codes, 3 Python codes, 5 tables, 10 exercises, 14 figures, and 52 references
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