Diffusion of directed polymers in a strong random environment
Diffusion of directed polymers in a strong random environment
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定向聚合物在强随机环境中的扩散
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
R. Song
中科院分区：
文献类型：
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作者：
P. Olsen;R. Song
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。 Imbrie 和 Spencer 表明，在空间维度为 3 或更高时，如果定向聚合物与环境相互作用较弱并且随机环境遵循伯努利分布，则行为是扩散的。在与 Imbrie 和 Spencer 相同的随机环境假设下，我们确定在空间维度为 4 或更高时，即使定向聚合物与环境发生强烈相互作用，行为仍然是扩散的。更一般地，我们可以证明，如果随机环境是有界的，并且如果分布支持的上界具有正质量，则存在整数 0 ，使得在高于 d 0 的维度中，随机聚合物的行为始终是扩散的。
We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. It was shown by Imbrie and Spencer that in spatial dimensions three or above the behavior is diffusive if the directed polymer interacts weakly with the environment and if the random environment follows the Bernoulli distribution. Under the same assumption on the random environment as that of Imbrie and Spencer, we establish that in spatial dimensions four or above the behavior is still diffusive even when the directed polymer interacts strongly with the environment. More generally, we can prove that, if the random environment is bounded and if the supremum of the support of the distribution has a positive mass, then there is an integerd0 such that in dimensions higher thand0 the behavior of the random polymer is always diffusive.