Geodesic
Central limit theorem for the spectrum of random Jacobi's matrices
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 513-522

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We consider the Jacobi's difference operator (infinite-dimensional matrix) such that the random variables on its main diagonal are independent and identically distributed with continuous density having compact support. The spectral properties of this operator are studied and the central limit theorem for the spectral distribution function is proved. 
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     author = {A. Ja. Reznikova},
     title = {Central limit theorem for the spectrum of random {Jacobi's} matrices},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {513--522},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a5/}
}
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A. Ja. Reznikova. Central limit theorem for the spectrum of random Jacobi's matrices. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 513-522. http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a5/