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The canonical spectral equation for singular spectral functions of random matrices. (English. Russian original) Zbl 0801.60055
Russ. Math. Surv. 48, No. 3, 163-179 (1993); translation from Usp. Mat. Nauk 48, No. 3(291), 163-180 (1993).
The author considers the problem to find equations for the Stieltjes transforms of singular spectral functions of random matrices of a large order, whose elements are independent and have their variances bounded by some constant. Starting from the formulae published earlier by the same author [Random matrices (1975; Zbl 0344.60001)], the solution of the problem is derived. The resultant equation, called canonical spectral equation, is valid for random matrices of a general form and often useful in applications.
MSC:
60H25 Random operators and equations (aspects of stochastic analysis)
60E99 Distribution theory
15B52 Random matrices (algebraic aspects)
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