Infrared Analysis of the Tridimensional Gross Neveu Model : Pointwise Bounds for the E ective

Within the context of renormalization group analysis, we describe how to get a minute control of the eeective potential theory for some fermionic systems using the tree expansion technique. We consider the tridimensional Gross-Neveu model (with smooth ultraviolet cut-oo) and present pointwise bounds for all the k-point kernels of the eeective potential after n steps of the renormalization group transformation. We still prove, for these kernels, the analycity in the initial interaction parameters (with an upper bound for the convergence radius independent on the volume), and the polynomial decay (in a well precise sense) as the distance between points becomes large. We use these results to study the k-point truncated correlation functions of the model in a separated paper PPO].