Entropy | |
On Products of Random Matrices | |
Natalia Amburg1  Dmitry Vasiliev1  Aleksander Orlov2  | |
[1] A.I. Alikhanov Institute for Theoretical and Experimental Physics of NRC Kurchatov Institute, B. Cheremushkinskaya, 25, 117259 Moscow, Russia;Institute of Oceanology, Nahimovskii Prospekt 36, 117997 Moscow, Russia; | |
关键词: random complex and random unitary matrices; matrix models; products of random matrices; Schur polynomial; Hurwitz number; generalized hypergeometric functions; | |
DOI : 10.3390/e22090972 | |
来源: DOAJ |
【 摘 要 】
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.
【 授权许可】
Unknown