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On High-Level Exceedances of Gaussian Fields and the Spectrum of Random Hamiltonians

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Abstract

We study the almost sure asymptotic structure of high-level exceedances by Gaussian random field ξ(x), x∈V with correlated values, where {V} is a family of ν-dimensional cubes increasing to Z ν. The results are applied to the study of the asymptotic behaviour of extreme eigenvalues of random Schrödinger operator in V.

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References

  1. Adler, R. L.: An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, Institute of Mathematical Statistics, Hayward, California, 1990.

    Google Scholar 

  2. Astrauskas, A.: On high-level exceedances of i.i.d. random fields, Statist. Probab. Lett. 52(2001), 271–277.

    Google Scholar 

  3. Astrauskas, A.: Extremal theory for spectrum of random discrete Schrödinger operator, Preprint No. 2002-26, Institute of Mathematics and Informatics, Vilnius, Lithuania, 2002.

  4. Astrauskas, A. and Molchanov, S. A.: Limit theorems for the ground states of the Anderson model, Functional Anal. Appl. 26(1992), 305–307.

    Google Scholar 

  5. Berman, S. M.: Limit theorems for the maximum term in stationary sequences, Ann. Math. Statist. 35(1964), 502–516.

    Google Scholar 

  6. Berman, S. M.: Sojourns and Extremes of Stochastic Processes, Wadsworth and Brooks/Cole, Pacific Grove, CA, 1992.

    Google Scholar 

  7. Leadbetter, M. R., Lindgren, G. and Rootzén, H.: Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, New York, 1983.

    Google Scholar 

  8. McCormick, W. P. and Reeves, J.: A weak convergence result for the maxima of consecutive minima for stationary processes, Comm. Statist. Stochastic Models 3(2) (1987), 159–172.

    Google Scholar 

  9. Mittal, Y. and Ylvisaker, D.: Limit distributions for the maxima of stationary Gaussian processes, Stochastic Process. Appl. 3(1975), 1–18.

    Google Scholar 

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  1. A. Astrauskas
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Astrauskas, A. On High-Level Exceedances of Gaussian Fields and the Spectrum of Random Hamiltonians. Acta Applicandae Mathematicae 78, 35–42 (2003). https://doi.org/10.1023/A:1025723719135

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  • DOI: https://doi.org/10.1023/A:1025723719135

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