Conditional Expectations and Renormalization

Details Conditional Expectations and Renormalization Conditional Expectations and Renormalization

2002-04-17

arxiv.org/abs/math-ph/0204038v1

Physics

Mathematical Physics

18 pages, includes 5 figures

Scientific paper

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 Monte-Carlo. 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.

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