Polymer Measure: Varadhan's Renormalization Revisited
Wolfgang Bock, Maria Jo\~ao Oliveira, Jos\'e Luis da Silva, Ludwig, Streit
TL;DR
This paper improves the understanding of how quickly the centered approximate self-intersection local time of planar Brownian motion converges, using chaos decomposition to refine Varadhan's estimate.
Contribution
It introduces an improved estimate for the convergence rate of the self-intersection local time of planar Brownian motion through chaos decomposition.
Findings
Enhanced convergence rate estimate for self-intersection local time
Application of chaos decomposition to refine Varadhan's estimate
Better understanding of planar Brownian motion self-intersections
Abstract
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.
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