论文标题
在时间依赖的随机重置下，在复杂网络上随机步行
Random walks on complex networks under time-dependent stochastic resetting
论文作者
论文摘要
我们研究了经过时间依赖性随机重置的网络上的离散时间随机步行，在该网络上，步行者要么在概率$ 1- ϕ（a）$的相邻节点之间随机跳动，要么将其重置为具有互补概率$ ϕ（a）$的给定节点。重置概率$ ϕ（a）$取决于自上次重置事件以来的时间$ a $（也称为Walker的年龄）。使用过渡矩阵的续订方法和光谱分解，我们将每个节点处沃克的固定职业概率以及任意两个节点之间的平均第一个通道时间。具体而言，我们认为两种完全可以解决的时间依赖性的重置协议。一个是$ ϕ（a）$是$ a $的阶梯形函数，另一个是$ ϕ（a）$是$ a $的合理函数。我们在两个不同的网络上演示了理论结果，也通过数值模拟验证，发现时间调制的重置协议比恒定概率重置在加速目标搜索过程中的恒定概率重置更有利。
We study discrete-time random walks on networks subject to a time-dependent stochastic resetting, where the walker either hops randomly between neighboring nodes with a probability $1-ϕ(a)$, or is reset to a given node with a complementary probability $ϕ(a)$. The resetting probability $ϕ(a)$ depends on the time $a$ since the last reset event (also called $a$ the age of the walker). Using the renewal approach and spectral decomposition of transition matrix, we formulize the stationary occupation probability of the walker at each node and the mean first passage time between arbitrary two nodes. Concretely, we consider that two different time-dependent resetting protocols that are both exactly solvable. One is that $ϕ(a)$ is a step-shaped function of $a$ and the other one is that $ϕ(a)$ is a rational function of $a$. We demonstrate the theoretical results on two different networks, also validated by numerical simulations, and find that the time-modulated resetting protocols can be more advantageous than the constant-probability resetting in accelerating the completion of a target search process.
