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Spectral theory of random self-adjoint operators

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Abstract

The survey reviews recent results on spectral analysis of differential and finite-difference operators with random spatially homogeneous coefficients. The corresponding problems that crystallized in the development of a number of areas in mathematics and related sciences are very rich and diverse. We discuss the traditional problems of spectral analysis, where the use of probabilistic ideas and methods now allows highly detailed spectral analysis to be performed for an essentially broader class of operators, as well as new problems and results obtained in the framework of this theory.

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Literature cited

Publications in Russian and Russian translations

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Publications in other languages

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Translated from Itogi Nauki i Tekhniki, Seriya Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 25, pp. 3–67, 1987.

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Pastur, L.A. Spectral theory of random self-adjoint operators. J Math Sci 46, 1979–2021 (1989). https://doi.org/10.1007/BF01096021

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Keywords

  • Spectral Analysis
  • Recent Result
  • Spectral Theory
  • Probabilistic Idea
  • Broad Class