A new hierarchy of upper and lower bounds on expectation values |
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Authors: | U Brandt J Stolze |
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Institution: | (1) Institut für Physik der Universität, Otto-Hahn-Strasse, Postfach 500500, D-4600 Dortmund, Federal Republic of Germany |
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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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