Estimates of general Mayer graphs. I. Construction of upper bounds for a given graph by means of sets of subgraphs. III. Upper bounds obtained by means of spanning n-trees. IV. On the computation of Gaussian integrals by star-mesh transformation
This series of papers reviews various applications of Mayer expansions and methods of estimating individual integrals and their sums. (Part II was published first [J. Statist. Phys. 19, 429-451 (1978; Zbl 0574.05048)] and deals with ionised systems.) Parts I and III introduce and discuss various methods of obtaining bounds for a given integral (by replacing the integrand by products of simpler integrands and using inequalities of Hölder type). Part IV introduces a new method, the ''star-mesh'' transformation, of calculating Mayer integrals whose integrands are Gaussian functions. This is much quicker than previously known methods. One of the previously used methods of estimation is tested on a Gaussian integral. \{Reviewer's remark: In the opinion of the reviewer the upper bound obtained is very poor. Since, as the author recognises, Mayer integrals nearly cancel one another for realistic interactions, very accurate estimates of individual integrals are needed.\}
scientific article; zbMATH DE number 3916326
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