Polymer measure: varadhan's renormalization revisited

Through chaos decomposition we improve the Varadhan estimate for the rate of convergence of the centered approximate self-intersection local time of planar Brownian motion.Financial support of FCT through the research project PTDC/MAT-STA/1284/2012 is gratefully acknowledged. W. B. and J. L. S. also would like to thank for financial support of IGK and DFG through SFB-701 (University of Bielefeld), respectively