具窄楔初始条件的抛物Anderson模型的空间渐近下界
概率论
2023-11-27 v1
摘要
设 为具窄楔初始条件的抛物 Anderson 模型的解。利用抛物 Anderson 模型的关联性质，我们建立了该解空间渐近的下界：\begin{align*} \liminf_{R\to\infty}\frac{ \max_{|x|\leq R}\left(\log u(t\,,x) + \frac{x^2}{2t}\right)}{(\log R)^{2/3}} \geq \frac14\left(\frac{t}2\right)^{1/3}, \quad \text{a.s.} \end{align*}
关键词
引用
@article{arxiv.2311.14243,
title = {Lower bound on spatial asymptotic of parabolic Anderson model with narrow wedge initial condition},
author = {Fei Pu},
journal= {arXiv preprint arXiv:2311.14243},
year = {2023}
}