Polymers in a weak random potential in dimension four: Rigorous renormalization group analysis

Correlation functions of the Edwards model of polymers at weak coupling are defined and studied at the critical point, in dimension four, by a rigorous renormalization group method which validates, at any order, perturbative renormalization group results on their behaviour at large distances. Remainders are controlled by a new argument which enlarges the use of methods of constructive field theory to models of statistical physics.A large part of this work has also included the collaboration of D. Arnaudon