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arXiv · 1902.04930

The scaling limits for Wiener sausages in random environments

Chien-Hao Huang
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Abstract

We consider the statistical mechanics of a random polymer with random walks and disorders in $\mathbb{Z}^d$. The walk collects random disorders along the way and gets nothing if it visits the same site twice. In the continuum and weak disorder regime, the partition function as a random variable converges weakly to a Wiener Chaos expansion when the dimension is lower than the critical dimension, which is four. A finite temperature case in one dimension is also discussed. The last case suggests that the end-point behavior of the polymer is $t^{2/3}$.

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Chien-Hao Huang. 2019-02-13. The scaling limits for Wiener sausages in random environments. https://arxiv.org/abs/1902.04930

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