Solvable Matrix Models

V. A. Kazakov

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Solvable Matrix Models

V. A. Kazakov

High Energy Physics - Theory · Submitted 8 Mar 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We review some old and new methods of reduction of the number of degrees of freedom from ~N^2 to ~N in the multi-matrix integrals.

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What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.40 · compares with prior results 0.26 · mentions code or data availability 0.02.

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We review some old and new methods of reduction of the number of degrees of freedom from ~N^2 to ~N in the multi-matrix integrals.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We review some old and new methods of reduction of the number of degrees of freedom from ~N^2 to ~N in the multi-matrix integrals.	contribution 0.87	0.19	0.24	asserted 0.78

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Original abstract

We review some old and new methods of reduction of the number of degrees of freedom from ~N^2 to ~N in the multi-matrix integrals.

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References

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Statistical physics of deep learning: Optimal learning of a multi-layer perceptron near interpolation
stat.ML 2025-10 conditional novelty 8.0 of 10

A replica/HCIZ theory predicts the Bayes-optimal generalization error of proportional-width MLPs near interpolation and discovers layer-wise specialization transitions that make deeper targets harder to learn.
Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model
hep-th 2021-08 conditional novelty 7.0 of 10

A relaxation step converts the nonlinear bootstrap of large-N multi-matrix integrals into a tractable convex program, and for the one-matrix model the positivity constraint is proved equivalent to a physical, real-sup...
Bootstraps to Strings: Solving Random Matrix Models with Positivity
hep-th 2020-02 accept novelty 7.0 of 10

Combining large-N loop equations with positivity of the correlator matrix pins random matrix model correlation functions to a tiny region, reproducing exact single-matrix solutions and constraining an unsolved two-mat...
Phases in WLZZ Matrix Models
hep-th 2025-07 conditional novelty 6.0 of 10

For WLZZ two-matrix models, integration contours describe only a finite-N subspace of Ward identity solutions, and the full solution space is recovered only in the N-to-infinity limit.

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12 arXiv papers cite this in 17 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Cites it as background 11 papers

Moving closer to the point, we only refer to works on the use of random matrices in [ref] , works about products of complex random matrices [ref] , a review [ref] and works close to ours from a mathematical point of view [ref] .

On Products of Random Matrices · Introduction · 0.97
Then, in the large $N$ limit, the problem can be reduced to the saddle point calculation, significantly simplifying the problem of computation of that functional integral.[An (incomplete) review of such solvable matrix models can be found in [ref] . ] The basic example of such a simplification is the one matrix model [equation] solvable for any potential $V(x)$.

Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model · Introduction · 0.98
This work appears as a result of the cross study of three topics: integrable hierarchies [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , matrix models [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] products of random matrices [ref] , [ref] , [ref] , [ref] and Hurwitz numbers in case of orientable surfaces [ref] , [ref] , [ref] , [ref] , [ref] - [ref] , [ref] , [ref] , [ref] and also of nonorientable ones [ref] - [ref] , [ref] , [ref] , [ref] .

Integrals of tau functions · Introduction · 1.00

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