We analyze large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time $t$ depends itself on the value $q_t$ of the time-averaged quantity. First we consider the elephant random walk and a Gaussian variant of this model, identifying two mechanisms for unusual fluctuation behavior, which differ from the Markovian case. In particular, the memory can lead to large-deviation principles with reduced speeds and to nonanalytic rate functions. We then explain how the mechanisms operating in these two models are generic for memory-dependent dynamics and show other examples including a non-Markovian simple exclusion process.

中文翻译：

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巨大的飞跃和长途旅行：具有远程记忆的系统中的波动机制。

我们使用随机存储器分析随机过程中时间平均量的较大偏差，其中时间动态 $Ť$ 取决于价值 $q_{Ť}$平均时间的数量。首先，我们考虑大象的随机行走和该模型的高斯变体，确定了异常波动行为的两种机理，这与马尔可夫现象不同。尤其是，存储器可能导致速度降低的大偏差原理以及非解析速率函数。然后，我们解释在这两个模型中运行的机制对于依赖于存储器的动力学如何通用，并显示其他示例，包括非马尔可夫简单排除过程。