Universality in marginally relevant disordered systems
Universality in marginally relevant disordered systems
复制标题
边缘相关无序系统中的普遍性
DOI：
10.1214/17-aap1276
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发表时间：
2015
影响因子：
1.8
通讯作者：
Nikos Zygouras
中科院分区：
文献类型：
--
作者：
F. Caravenna;Rongfeng Sun;Nikos Zygouras
我们考虑定向聚合物类型的无序系统，其中无序是所谓的边缘相关。这些模型包括（2+1）维的短程定向聚合物模型、（1+1）维的具有Cauchy尾的长程定向聚合物模型和尾指数为1/2的无序钉扎模型。我们表明，在一个适当的弱无序和连续极限，这些不同的模型的配分函数收敛到一个普遍的极限：一个对数正态随机场与多尺度相关结构，它经历了相变的无序强度的变化。作为一个副产品，我们表明，二维随机热方程的解决方案，适当的正则化，收敛到相同的限制。该证明使用了著名的第四矩定理，揭示了上述类别中所有模型所共有的有趣的混乱结构。
We consider disordered systems of directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2+1), the long-range directed polymer model with Cauchy tails in dimension (1+1) and the disordered pinning model with tail exponent 1/2. We show that in a suitable weak disorder and continuum limit, the partition functions of these different models converge to a universal limit: a log-normal random field with a multi-scale correlation structure, which undergoes a phase transition as the disorder strength varies. As a by-product, we show that the solution of the two-dimensional Stochastic Heat Equation, suitably regularized, converges to the same limit. The proof, which uses the celebrated Fourth Moment Theorem, reveals an interesting chaos structure shared by all models in the above class.
影响因子：
2.6
作者：
F. Caravenna;Rongfeng Sun;Nikos Zygouras
通讯作者：
F. Caravenna;Rongfeng Sun;Nikos Zygouras