On Products of Random Matrices
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....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/9/972 |
| _version_ | 1797555007886721024 |
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| author | Natalia Amburg Aleksander Orlov Dmitry Vasiliev |
| author_facet | Natalia Amburg Aleksander Orlov Dmitry Vasiliev |
| author_sort | Natalia Amburg |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T16:41:10Z |
| format | Article |
| id | doaj.art-ce63cfb241f04259a2c2f38eb0b6019d |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T16:41:10Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ce63cfb241f04259a2c2f38eb0b6019d2023-11-20T12:04:38ZengMDPI AGEntropy1099-43002020-08-0122997210.3390/e22090972On Products of Random MatricesNatalia Amburg0Aleksander Orlov1Dmitry Vasiliev2A.I. Alikhanov Institute for Theoretical and Experimental Physics of NRC Kurchatov Institute, B. Cheremushkinskaya, 25, 117259 Moscow, RussiaInstitute of Oceanology, Nahimovskii Prospekt 36, 117997 Moscow, RussiaA.I. Alikhanov Institute for Theoretical and Experimental Physics of NRC Kurchatov Institute, B. Cheremushkinskaya, 25, 117259 Moscow, RussiaWe 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.https://www.mdpi.com/1099-4300/22/9/972random complex and random unitary matricesmatrix modelsproducts of random matricesSchur polynomialHurwitz numbergeneralized hypergeometric functions |
| spellingShingle | Natalia Amburg Aleksander Orlov Dmitry Vasiliev On Products of Random Matrices Entropy random complex and random unitary matrices matrix models products of random matrices Schur polynomial Hurwitz number generalized hypergeometric functions |
| title | On Products of Random Matrices |
| title_full | On Products of Random Matrices |
| title_fullStr | On Products of Random Matrices |
| title_full_unstemmed | On Products of Random Matrices |
| title_short | On Products of Random Matrices |
| title_sort | on products of random matrices |
| topic | random complex and random unitary matrices matrix models products of random matrices Schur polynomial Hurwitz number generalized hypergeometric functions |
| url | https://www.mdpi.com/1099-4300/22/9/972 |
| work_keys_str_mv | AT nataliaamburg onproductsofrandommatrices AT aleksanderorlov onproductsofrandommatrices AT dmitryvasiliev onproductsofrandommatrices |