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A new hierarchy of upper and lower bounds on expectation values

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Zeitschrift für Physik B Condensed Matter

Abstract

Upper and lower bounds are constructe for expectation values of functions of a real random variable with derivatives up to orderN+1 which are alternately negative and positive over the whole range of interest. The bounds are given by quadrature formulas with weights and abscissas determined by the firstN+1 moments of the underlying probability distribution. Application to a simple disordered phonon system yields sharp bounds on the specific heat.

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Authors and Affiliations

  1. Institut für Physik der Universität, Otto-Hahn-Strasse, Postfach 500500, D-4600, Dortmund, Federal Republic of Germany

    U. Brandt & J. Stolze

Authors
  1. U. Brandt
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  2. J. Stolze
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Brandt, U., Stolze, J. A new hierarchy of upper and lower bounds on expectation values. Z. Physik B - Condensed Matter 43, 61–67 (1981). https://doi.org/10.1007/BF01295476

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  • DOI: https://doi.org/10.1007/BF01295476

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