具有缓变陷阱的Bouchaud陷阱模型的泛函极限定理
Functional limit theorems for 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。我们的主要结果是一个功能的极限定理的退火法律下的模型，类似的功能极限定理以前建立在文献中的情况下，可积或定期变化的陷阱分布。反映的事实，时钟过程是占主导地位的极限的贡献，从最深的访问陷阱，该模型的极限过程是一个空间从属的布朗运动，其相关的时钟过程是一个极值过程。
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. Our main result is a functional limit theorem for the model under the annealed law, analogous to the functional limit theorems previously established in the literature in the case of integrable or regularly varying trap distribution. Reflecting the fact that the clock process is dominated in the limit by the contribution from the deepest-visited trap, the limit process for the model is a spatially-subordinated Brownian motion whose associated clock process is an extremal process.
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