A Variational Characterization of the Speed of a One-Dimensional Self- Repellent Random Walk
A Variational Characterization of the Speed of a One-Dimensional Self- Repellent Random Walk
Let $Q^\alpha_n$ be the probability measure for an $n$-step random walk $(0,S_1,\ldots,S_n)$ on $\mathbb{Z}$ obtained by weighting simple random walk with a factor $1 - \alpha$ for every self-intersection. This is a model for a one-dimensional polymer. We prove that for every $\alpha \in (0,1)$ there exists $\theta^\ast(\alpha) \in (0,1)$ …