The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ’conformal’ (multicomponent) and Kontsevich models are considered in some detail, together with the Ward identites (’W-constraints’), determinantal formulas and continuum limits, taking one kind of model into another. Subtle points and directions of the future research are also discussed.

PACS: 02.10.+b, 11.17.+y DOI: 10.1070/PU1994v037n01ABEH000001 URL: https://ufn.ru/en/articles/1994/1/a/ A1994NA86300001 Citation: Morozov A Yu "Integrability and matrix models" Phys. Usp. 37 1–55 (1994) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Морозов А Ю «Интегрируемость и матричные модели» УФН 164 3–62 (1994); DOI: 10.3367/UFNr.0164.199401a.0003