Q1063010
type: Item
instance of: scholarly article
title: 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
zbMATH Open document ID: 0574.05049
DOI: 10.1007/BF01011094
author: Michel Lavaud
published in: Journal of Statistical Physics
publication date: 1982-01-01T00:00:00Z
review text: 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.\}
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 3916326
MaRDI profile type: Publication
cites work: Q5576969
cites work: Q5640289
cites work: Constructive quantum field theory. The 1973 'Ettore Majorana' international school of mathematical physics
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cites work: Estimates of general Mayer graphs. II. Long range behaviour of graphs with two root points occuring in the theory of ionized systems
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full work available at URL: https://doi.org/10.1007/bf01011094
OpenAlex ID: W2325325837
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label: 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
description: scientific article; zbMATH DE number 3916326