The continuum disordered pinning model.
The continuum disordered pinning model.
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DOI：
10.1007/s00440-014-0606-4
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发表时间：
2016
影响因子：
2
通讯作者：
Zygouras N
中科院分区：
文献类型：
--
作者：
Caravenna F;Sun R;Zygouras N
任何固定的a.s.稳定再生集的特性（例如，其Hausdorff维数）也是a.s. CDPM的属性，几乎每一个环境的实现。尽管如此，法律的CDPM是单一的法律方面的稳定再生集，几乎每一个实现的环境。任何更新过程的多项式尾部，指数，有一个非平凡的标度极限，称为稳定再生集。在本文中，我们考虑这样的更新过程中的独立同分布的吉布斯变换。随机环境，称为无序钉扎模型。我们发现，这些模型有一个普遍的标度限制，我们称之为连续无序钉扎模型（CDPM）。这是在白色噪声随机环境中的随机闭子集，具有微妙的特征：无序连续模型的存在，如CDPM，是钉扎模型的无序相关性的表现。
Any fixed a.s. property of the -stable regenerative set (e.g., its Hausdorff dimension) is also an a.s. property of the CDPM, for almost every realization of the environment. Nonetheless, the law of the CDPM is singular with respect to the law of the -stable regenerative set, for almost every realization of the environment. Any renewal processes on with a polynomial tail, with exponent , has a non-trivial scaling limit, known as the -stable regenerative set. In this paper we consider Gibbs transformations of such renewal processes in an i.i.d. random environment, called disordered pinning models. We show that for these models have a universal scaling limit, which we call the continuum disordered pinning model (CDPM). This is a random closed subset of in a white noise random environment, with subtle features: The existence of a disordered continuum model, such as the CDPM, is a manifestation of disorder relevance for pinning models with .