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Precise high energy asymptotics for the integrated density of states of an unbounded random Jacobi matrix. (English) Zbl 1044.82007

Summary: The purpose of this paper is to study the transition from the classical to the quantum asymptotics for the integrated density of states of an unbounded random Jacobi matrix. Therefore, we give precise results on the behavior of the tail of the integrated density of states near infinity. We study the evolution of these asymptotics when the decay of the tail of the distribution of the random potential increases.

MSC:

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
47B80 Random linear operators
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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[1] DOI: 10.1088/0305-4470/15/7/025 · Zbl 0492.60055 · doi:10.1088/0305-4470/15/7/025
[2] DOI: 10.1007/BF01017848 · doi:10.1007/BF01017848
[3] DOI: 10.1023/A:1023293423978 · Zbl 0924.47057 · doi:10.1023/A:1023293423978
[4] DOI: 10.1215/S0012-7094-99-09810-1 · Zbl 1060.82509 · doi:10.1215/S0012-7094-99-09810-1
[5] Lifshitz I. M., Soviet Phys. JETP 17 pp 1159– (1963)
[6] DOI: 10.1070/PU1965v007n04ABEH003634 · doi:10.1070/PU1965v007n04ABEH003634
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