具有缓变陷阱的Bouchaud陷阱模型中的两点局部化
Two-site localisation in the Bouchaud trap model with slowly varying traps
摘要：
我们考虑整数上的布绍陷阱模型，陷阱分布在无穷远处有一个缓慢变化的尾部。我们证明，该模型最终定位在两个网站上以压倒性的概率。这是一个更强的形式的本地化比以前已经建立在文献中的布绍陷阱模型的整数的情况下，定期变化的陷阱。这个结果的基础是这样一个事实，即i.i.d.具有缓变尾部的随机变量是由极大项渐近控制的。
英文摘要：
We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. We prove that the model eventually localises on exactly two sites with overwhelming probability. This is a stronger form of localisation than has previously been established in the literature for the Bouchaud trap model on the integers in the case of regularly varying traps. Underlying this result is the fact that the sum of a sequence of i.i.d. random variables with a slowly varying tail is asymptotically dominated by the maximal term.
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