The scaling limits for Wiener sausages in random environments

2019/02/13 by Chien‐Hao Huang, Huang, Chien-Hao · 1 citation
Mathematics · Physics and Astronomy · #60Fxx #60K37 (Primary) #82D30 (Secondary) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1902.04930

openalex publication_date 2019/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the statistical mechanics of a random polymer with random walks and disorders in 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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• Non-directed polymers in random environments with range penalties: the high dimensional case

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