%0 Journal Article
%T Finite Range Decomposition of Gaussian Processes
%+ Laboratoire de Physique Mathématique et Théorique (PMT)
%A Mitter, Pronob
%A Brydges, David
%A Guadagni, G.
%Z 26 pages, LaTeX, paper in honour of G.Jona-Lasinio.Typos corrected, corrections in section 5 and appendix A
%< avec comité de lecture
%Z 03-030
%@ 0022-4715
%J Journal of Statistical Physics
%I Springer Verlag
%V 115
%N 1/2
%P 415-449
%8 2004-04-04
%D 2004
%Z math-ph/0303013
%R 10.1023/B:JOSS.0000019818.81237.66
%K Gaussian processes
%K finite range decomposition
%K lattice
%K renormalization group
%K Lévy processes
%Z Physics [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]
%Z Sciences of the Universe [physics]/Astrophysics [astro-ph]Journal articles
%X 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
%G English
%L hal-00286525
%U https://hal.science/hal-00286525
%~ CNRS
%~ UNIV-MONTP2
%~ UNIV-MONTPELLIER
%~ UM1-UM2