A remark on diffusion of directed polymers in random environments
A remark on diffusion of directed polymers in random environments
复制标题
关于定向聚合物在随机环境中扩散的评论
DOI：
10.1007/bf02175566
复制
发表时间：
1996
影响因子：
1.6
通讯作者：
X. Zhou
中科院分区：
文献类型：
--
作者：
R. Song;X. Zhou
我们考虑随机游走或定向聚合物的系统与空间和时间随机的环境相互作用。在对环境分布的最小假设下，我们证明该系统具有扩散行为，概率为 1 ifd>2 且 β<β0，其中 β0 是根据 d 维整数格上的对称最近邻随机游走返回到其起点的概率来定义的。我们还获得了该系统均方位移的精确估计。
We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. Under minimal assumptions on the distribution of the environment, we prove that this system has diffusive behavior with probability one ifd>2 and β<β0, where β0 is defined in terms of the probability that the symmetric nearest neighbor random walk on thed-dimensional integer lattice ever returns to its starting point. We also obtain a precise estimate for the mean square displacement of this system.