Random walk in cooling random environment: Recurrence versus transience and mixed fluctuations
Random walk in cooling random environment: Recurrence versus transience and mixed fluctuations
复制标题
冷却随机环境中的随机游走：循环与瞬态和混合波动
DOI：
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发表时间：
2019
影响因子：
1.5
通讯作者：
F. Hollander
中科院分区：
文献类型：
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作者：
L. Avena;Y. Chino;C. D. Costa;F. Hollander
这是一系列论文中的第三篇，我们在其中考虑了冷却随机环境中的一维随机游动（RWCRE）。后者是通过从随机环境中的一维随机游走（RWRE）开始，并沿着一系列确定性时间（称为刷新时间）对环境进行刷新来获得的。在本论文中，我们探讨两个问题，一般刷新时间。首先，我们调查如何复发与瞬态标准已知的RWRE的RWCRE的变化。其次，我们探讨了波动RWCRE时，RWRE是经常性的或满足经典的中心极限定理。我们表明，答案取决于在一个微妙的方式选择的刷新时间。我们的论文的一个首要目标是研究一个具有丰富的相关结构的随机过程的行为如何受到重置的影响。
This is the third in a series of papers in which we consider one-dimensional Random Walk in Cooling Random Environment (RWCRE). The latter is obtained by starting from one-dimensional Random Walk in Random Environment (RWRE) and resampling the environment along a sequence of deterministic times, called refreshing times. In the present paper we explore two questions for general refreshing times. First, we investigate how the recurrence versus transience criterion known for RWRE changes for RWCRE. Second, we explore the fluctuations for RWCRE when RWRE is either recurrent or satisfies a classical central limit theorem. We show that the answer depends in a delicate way on the choice of the refreshing times. An overarching goal of our paper is to investigate how the behaviour of a random process with a rich correlation structure can be affected by resettings.