On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian Auteur(s): Mitter P. (Article) Publié: Journal Of Statistical Physics, vol. 163 p.1235-1246 (2016) Texte intégral en Openaccess : Ref HAL: hal-01338274_v1 Ref Arxiv: 1512.02877 DOI: 10.1007/s10955-016-1507-y WoS: WOS:000375579300009 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote 3 Citations Résumé: We prove the existence as well as regularity of a finite range decomposition for the resolvent $G_{\alpha} (x-y,m^2) = ((-\Delta)^{\alpha\over 2} + m^{2})^{-1} (x-y) $, for $0<\alpha<2$ and all real $m$, in the lattice ${\mathbf Z}^{d}$ as well as in the continuum ${\mathbf R}^{d}$ for dimension $d\ge 2$. This resolvent occurs as the covariance of the Gaussian measure underlying weakly self- avoiding walks with long range jumps (stable L\'evy walks) as well as continuous spin ferromagnets with long range interactions in the long wavelength or field theoretic approximation. The finite range decomposition should be useful for the rigorous analysis of both critical and off-critical renormalisation group trajectories. The decomposition for the special case $m=0$ was known and used earlier in the renormalisation group analysis of critical trajectories for the above models below the critical dimension $d_c =2\alpha$. Commentaires: 16 pages, 1 figure, typos corrected, corrected, reference added, one sentence added |