%0 Conference Proceedings
%T The Finite Range Renormalization Group
%+ Laboratoire Charles Coulomb (L2C)
%A Mitter, Pronob
%Z International Workshop at the Erwin Schroedinger International Institute for Mathematical Physics, University of Vienna.
%F Invité
%< avec comité de lecture
%Z L2C:11-190
%B The Rigorous Renormalization Group in the LHC era.
%C Vienne, Austria
%8 2011-09-20
%D 2011
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Mathematical Physics [math-ph]Conference papers
%X In this talk I will show that a large class of Gaussian Random Fields in the continuum or the lattice can be written as a sum of independent Gaussian random fields called fluctuation fields which enjoy the following properties: their covariances have finite range (compact support) and the fields are almost surely smooth. The fluctuation covariances satisfy very strong uniform bounds . After suitable rescaling the sequence of fluctuation fields converges in distribution to a a smooth continuum Gaussian random field whose covariance has finite range. This finite range multiscale expansion is the basis of a new mathematical form of Wilson's Renormalization Group where non local effects are minimized and estimates rendered simpler. In particular, on the lattice, this gives an alternative to the Kadanoff-Wilson renormalization group based on the block spin transformation. The talk is based on my joint work with D. Brydges and G. Guadagni (J. Stat.Phys. 115,415-449 (2004)) and a further paper with D. Brydges (2011, in preparation).
%G English
%L hal-00652868
%U https://hal.science/hal-00652868
%~ CNRS
%~ L2C
%~ TDS-MACS
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021