抛物型Anderson模型的部分重势去定域化
Delocalising the parabolic Anderson model through partial duplication of the potential
摘要：
在$\mathbb{Z}^d$上的抛物型Anderson模型，其i.i.d.如果势的分布在无穷远处是足够重尾的，则已知势完全局域化。在本文中，我们调查的模型，其中的潜在的部分复制在一个对称的方式通过原点的平面的修改。在多项式尾衰减的势分布的情况下，我们表现出令人惊讶的相变模型的衰减指数的变化。对于指数的大值，模型完全局部化，如在i.i.d.案子相比之下，对于小的指数值，我们表明，该模型可能离域。更确切地说，我们表明，有一个不可忽略的概率事件的解决方案具有不可忽略的质量上的两个网站。
英文摘要：
The parabolic Anderson model on $\mathbb{Z}^d$ with i.i.d. potential is known to completely localise if the distribution of the potential is sufficiently heavy-tailed at infinity. In this paper we investigate a modification of the model in which the potential is partially duplicated in a symmetric way across a plane through the origin. In the case of potential distribution with polynomial tail decay, we exhibit a surprising phase transition in the model as the decay exponent varies. For large values of the exponent the model completely localises as in the i.i.d. case. By contrast, for small values of the exponent we show that the model may delocalise. More precisely, we show that there is an event of non-negligible probability on which the solution has non-negligible mass on two sites.
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