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On Products of Random Matrices

1
A.I. Alikhanov Institute for Theoretical and Experimental Physics of NRC Kurchatov Institute, B. Cheremushkinskaya, 25, 117259 Moscow, Russia
2
Institute for Information Transmission Problems of RAS (Kharkevich Institute), Bolshoy Karetny per. 19, build.1, 127051 Moscow, Russia
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Moscow Center for Fundamental and Applied Mathematics, 119991 Moscow, Russia
4
Institute of Oceanology, Nahimovskii Prospekt 36, 117997 Moscow, Russia
5
Moscow Institute of Physics and Technology, 141701 Dolgoprudny, Russia
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(9), 972; https://doi.org/10.3390/e22090972
Received: 6 July 2020 / Revised: 16 August 2020 / Accepted: 17 August 2020 / Published: 31 August 2020
(This article belongs to the Special Issue Random Matrix Approaches in Classical and Quantum Information Theory)
We introduce a family of models, which we name matrix models associated with children’s drawings—the so-called dessin d’enfant. Dessins d’enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky). The vertices of such a graph are small disks that we call stars. We attach random matrices to the edges of the graph and get multimatrix models. Additionally, to the stars we attach source matrices. They play the role of free parameters or model coupling constants. The answers for our integrals are expressed through quantities that we call the “spectrum of stars”. The answers may also include some combinatorial numbers, such as Hurwitz numbers or characters from group representation theory. View Full-Text
Keywords: random complex and random unitary matrices; matrix models; products of random matrices; Schur polynomial; Hurwitz number; generalized hypergeometric functions; integrable systems random complex and random unitary matrices; matrix models; products of random matrices; Schur polynomial; Hurwitz number; generalized hypergeometric functions; integrable systems
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MDPI and ACS Style

Amburg, N.; Orlov, A.; Vasiliev, D. On Products of Random Matrices. Entropy 2020, 22, 972.

AMA Style

Amburg N, Orlov A, Vasiliev D. On Products of Random Matrices. Entropy. 2020; 22(9):972.

Chicago/Turabian Style

Amburg, Natalia; Orlov, Aleksander; Vasiliev, Dmitry. 2020. "On Products of Random Matrices" Entropy 22, no. 9: 972.

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