Conditional Expectations and Renormalization
Abstract
In optimal prediction methods one estimates the future behavior of underresolved systems by solving reduced systems of equations for expectations conditioned by partial data; renormalization group methods reduce the number of variables in complex systems through integration of unwanted scales. We establish the relation between these methods for systems in thermal equilibrium, and use this relation to find renormalization parameter flows and the coefficients in reduced systems by expanding conditional expectations in series and evaluating the coefficients by MonteCarlo. We illustrate the construction by finding parameter flows for simple spin systems and then using the renormalized (=reduced) systems to calculate the critical temperature and the magnetization.
 Publication:

arXiv eprints
 Pub Date:
 April 2002
 DOI:
 10.48550/arXiv.mathph/0204038
 arXiv:
 arXiv:mathph/0204038
 Bibcode:
 2002math.ph...4038C
 Keywords:

 Mathematical Physics;
 82B28;
 65C05;
 60K10;
 65C40;
 76F55
 EPrint:
 18 pages, includes 5 figures