论文标题
在随机重置的情况下，在随机网络上随机步行有偏见：精确结果
Biased random walk on random networks in presence of stochastic resetting: Exact results
论文作者
论文摘要
我们考虑在随机梳子上构成的随机网络上有偏见的随机步行，该梳子包含带有静止的随机长度分支的主链。骨干和分支朝着偏置的方向延伸。对于裸模型，当模型受到随机重置时，分支上的步行者以恒定的速率重置到相应的主链位点时，我们获得了确切的固态静态和动态性能，以实现给定的疾病，以实现在任意分布后采样的分支长度。我们得出一个标准，可以在固定状态下观察一个沿主链的非零漂移速度。对于裸露的模型，我们讨论了非单调的漂移速度的发生，该速度是偏见的函数，由于步行者被困在很长的分支上，因此变为零超出阈值偏差。此外，我们表明重置使系统能够逃脱捕获，从而导致漂移速度在任何偏见时都是有限的。
We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as also when the model is subject to stochastic resetting, whereby the walkers on the branches reset with a constant rate to the respective backbone sites, we obtain exact stationary-state static and dynamic properties for a given disorder realization of branch lengths sampled following an arbitrary distribution. We derive a criterion to observe in the stationary state a non-zero drift velocity along the backbone. For the bare model, we discuss the occurrence of a drift velocity that is non-monotonic as a function of the bias, becoming zero beyond a threshold bias because of walkers trapped at very long branches. Further, we show that resetting allows the system to escape trapping, resulting in a drift velocity that is finite at any bias.
