论文标题
连续时间弱避免自我避免的步行$ \ mathbb {z} $严格单调逃生速度
Continuous-time weakly self-avoiding walk on $\mathbb{Z}$ has strictly monotone escape speed
论文作者
论文摘要
虚弱的自我避免步行（WSAW）是一种简单的随机步行路径的模型，可以惩罚自身交流。在$ \ mathbb {z} $上，格雷文（Greven）和丹·霍兰德（Den Hollander）在1993年证明，离散的时间弱避免自我避免的步行具有渐近确定性的逃生速度，他们猜想这种速度应严格增加驱虫强度参数。我们研究了该模型的连续时间版本，为速度提供了不同的存在证明，并证明了严格提高的速度。该证明使用通过BFS的超对称版本实现的转移矩阵方法 - 二氧化基定理，光谱理论，Tauberian理论和随机优势。
Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On $\mathbb{Z}$, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing. The proof uses a transfer matrix method implemented via a supersymmetric version of the BFS--Dynkin isomorphism theorem, spectral theory, Tauberian theory, and stochastic dominance.
