Chaos expansion of 2D parabolic Anderson model
Yu Gu, Jingyu Huang
TL;DR
This paper develops a chaos expansion for the 2D parabolic Anderson model in small time, linking the expansion coefficients to the annealed density of a polymer in white noise, advancing understanding of stochastic PDEs.
Contribution
It introduces a novel chaos expansion for the 2D parabolic Anderson model with coefficients related to polymer densities in white noise environments.
Findings
Established chaos expansion for the model
Connected expansion coefficients to polymer annealed densities
Provides new analytical tools for stochastic PDE analysis
Abstract
We prove a chaos expansion for the 2D parabolic Anderson Model in small time, with the expansion coefficients expressed in terms of the annealed density function of the polymer in a white noise environment.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Advanced Mathematical Modeling in Engineering