论文标题
离散时空重置模型：应用于第一步和传输统计
Discrete space-time resetting model: Application to first-passage and transmission statistics
论文作者
论文摘要
我们考虑带有重置的晶格随机步行的动力学。步行者在任意维度的晶格上随机移动，每个时间步长将其重置为具有恒定概率$ r $的给定站点。我们构建一个离散的续订方程，并根据基础无复位的传播器或Green的功能来构建不同量的重置动力学的闭合形式表达式。我们将形式主义应用于一维无限空间中偏见的随机行走动力学，并显示一个人如何在连续限制中恢复，从而通过重置扩散。还分析了与周期性和反射边界界定的一维域中有偏见的随机步行者的重置动力学。根据偏差，周期域中的第一阶段概率显示出多折非单调性，因为$ r $是多种多样的。最后，我们将形式主义应用于研究两个晶格步行者的传播动力学，并在一维域中重置，并以周期性和反映边界为界。随着重置概率的变化，步行者之间明确传播的概率显示出非单调的行为。
We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability $r$. We construct a discrete renewal equation and present closed-form expressions for different quantities of the resetting dynamics in terms of the underlying reset-free propagator or Green's function. We apply our formalism to the biased random walk dynamics in one-dimensional unbounded space and show how one recovers in the continuous limits results for diffusion with resetting. The resetting dynamics of biased random walker in one-dimensional domain bounded with periodic and reflecting boundaries is also analyzed. Depending on the bias the first-passage probability in periodic domain shows multi-fold non-monotonicity as $r$ is varied. Finally, we apply our formalism to study the transmission dynamics of two lattice walkers with resetting in one-dimensional domain bounded by periodic and reflecting boundaries. The probability of a definite transmission between the walkers shows non-monotonic behavior as the resetting probabilities are varied.
