Gaussian Fluctuation for Superdiffusive Elephant Random Walks
Gaussian Fluctuation for Superdiffusive Elephant Random Walks
复制标题
DOI：
10.1007/s10955-019-02414-0
复制
发表时间：
2019-09
影响因子：
1.6
通讯作者：
Naoki Kubota;Masato Takei
中科院分区：
文献类型：
--
作者：
Naoki Kubota;Masato Takei
大象随机游走是一种具有无限记忆的一维离散时间随机游走：对于每一步，步行者都有概率采用他/她之前随机选择的步骤之一，否则他/她的表现就像简单的随机游走（可能带有偏差）。它允许在临界值处从扩散行为到超扩散行为的相变。因为，存在一个阶比例因子，使得步行者的位置在时间尺度上收敛为非简并随机变量，其分布不是高斯分布。我们的主要结果表明，周围的波动仍然是高斯的。我们还描述了由偏置随时间多项式衰减引起的相变。
Elephant random walk is a kind of one-dimensional discrete-time random walk with infinite memory: For each step, with probabilitythe walker adopts one of his/her previous steps uniformly chosen at random, and otherwise he/she performs like a simple random walk (possibly with bias). It admits a phase transition from diffusive to superdiffusive behavior at the critical value. For, there is a scaling factorof ordersuch that the positionof the walker at timenscaled byconverges to a nondegenerate random variable, whose distribution is not Gaussian. Our main result shows that the fluctuation ofaroundis still Gaussian. We also give a description of a phase transition induced by bias decaying polynomially in time.