Ref HAL: hal-00286525_v1
Ref Arxiv: math-ph/0303013
DOI: 10.1023/B:JOSS.0000019818.81237.66
WoS: 000220250600020
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
33 Citations
Résumé:

Let Delta be the finite difference Laplacian associated to the lattice Z d . For dimension dge3, age0, and L a sufficiently large positive dyadic integer, we prove that the integral kernel of the resolvent G a colone(a–Delta)–1 can be decomposed as an infinite sum of positive semi-definite functions V n of finite range, V n (x–y)=0 for |x–y|geO(L) n . Equivalently, the Gaussian process on the lattice with covariance G a admits a decomposition into independent Gaussian processes with finite range covariances. For a=0, V n has a limiting scaling form $$L^{ - n\left( {d - 2} \right)} \Gamma _{c,*} \left( {\tfrac{{x - y}}{{L^n }}} \right)$$ as nrarrinfin. As a corollary, such decompositions also exist for fractional powers (–Delta)–agr/2, 0

Commentaires: 26 pages, LaTeX, paper in honour of G.Jona-Lasinio.Typos corrected, corrections in section 5 and appendix A