论文标题
巨型飞跃和长途旅行：具有远距离记忆的系统中的波动机制
Giant leaps and long excursions: fluctuation mechanisms in systems with long-range memory
论文作者
论文摘要
我们分析了具有远距离内存的随机过程中时间平均数量的巨大偏差，其中时间t的动力学取决于时间平均数量的值q_t。首先，我们考虑大象随机步行和该模型的高斯变体，确定了两种与马尔可夫情况不同的异常波动行为的机制。特别是，内存可以导致速度降低的较大偏差原理和非分析速率函数。然后，我们解释了这两个模型中运行的机制如何对内存依赖性动力学进行通用，并显示其他示例，包括非马克维亚对称排除过程。
We analyse 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 behaviour, which differ from the Markovian case. In particular, the memory can lead to large deviation principles with reduced speeds, and to non-analytic 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 symmetric exclusion process.
