Chaos Decomposition and Gap Renormalization of Brownian Self-Intersection Local Times
Jinky Bornales, Maria Jo\~ao Oliveira, Ludwig Streit
TL;DR
This paper investigates the chaos decomposition and regularization of Brownian self-intersection local times, focusing on Varadhan's renormalization within the planar Edwards model to better understand their mathematical structure.
Contribution
It introduces a novel approach to chaos decomposition and gap renormalization of self-intersection local times, advancing the theoretical understanding of the planar Edwards model.
Findings
Established a new chaos decomposition framework for self-intersection local times
Developed a regularization method aligned with Varadhan's renormalization
Enhanced the mathematical understanding of the planar Edwards model
Abstract
We study the chaos decomposition of self-intersection local times and their regularization, with a particular view towards Varadhan's renormalization for the planar Edwards model.
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